non specific excuse!

There isnt a ton of canon material to go off of with these two, so mostly im extrapolating based on the consequences of the interaction that does get shown. Namely, bill calling for their help, and the axolotl sending him to theraprism. There are a few other hints as to what they think of each other within the axolotl's poems, bill's coded remarks about the "big frilly know it all," and the frilliam pages. They are said to be opposites, as well as old friends, and the axolotl is obviously a lot more powerful than bill/implied to be god. In j3 bill is contemptuous towards them like any other authority figure, but he ultimately still knows when to ask for their help, and they are willing to help him.

Now, "opposites" could be interpreted in a lot of ways. Often i see people interpret this as the axolotl being a pure benevolent being of harmony to oppose bill's evil and chaos, but i think this is a reductive way of examining bill's character. Yes he's chaotic and malicious, but understanding his motives, and using those to extrapolate the axolotl's motives, gives a more well rounded idea of who and what the axolotl is.

Some examples:

Bill wants power, he spends his whole existence chasing after it, so his opposite is someone who has power and never had to work for it. Bill starts out as a little fish in a big big pond, his opposite is a big fish.

Bill wants to be understood and accepted, his opposite has no interest in that. The axolotl is opaque; you can ask them one question, and they are going to answer you with a riddle.

Bill wants control. His opposite is able to go with the flow and, for the most part, let the universe run its course. Even though the axolotl is painted as an omnipotent and omnipowerful being, we don't see them do much with that. They know about the havoc bill continually wreaks, and they don't bother stopping him. The one intervention we see is them saving bill from death.

I adore the hc that bill is simply the axolotl's specialest little guy, and i think its supported by what i just mentioned. Even if we look at them flatly as a chaos god and a harmony god, what is the harmony god doing to keep the peace? Not much that we can see. Instead we see them preserving a force of chaos and giving him a second chance just because he asked so niceys.

I like bill and the axolotl's relationship best when it can be a parallel to bill and ford's relationship. The oroborous could be the two opposing forces of harmony and chaos chasing one another, but it could also be a self-perpetuating cycle, and i like that second one better. Lots more fun. I love a good cycle.

So now lets take what we worked out in analysis land and bring it over to headcanon land. Take my hand it'll be fun.

To get them to a point where they can parallel bill and ford, bill has to trust the axolotl at some point. I think early on, directly after euclydia was destroyed, when he was suddenly alone in the universe (isolated like ford was), scared and without a clear direction, he met the axolotl. He was wowed by them, not by any flashy tricks on the axolotl's part but simply by the fact of their existence. They were the first higher dimensional being he ever met. And of course, he trusted them. He had no one else to trust. And the axolotl formed an attachment to him in turn. Maybe they're the only one of their kind too, maybe no one was supposed to survive the 2nd dimension incident, and they're impressed by bill as a living anomaly. Bill, aware of the axolotl's abilities, asked for their help and they said yes, only, it wasn't the kind of help he wanted.

I don't see bill and the axolotls relationship as romantic on either side, more like a mentor/mentee, or a sort of caretaker relationship. I also think bill was young when euclydia was destroyed, a teenager or a young adult, so he unconsciously latches onto the axolotl as a parental figure when he is freshly an orphan. He wants to trust them. He doesn't want to be alone. The axolotl might provide some guidance to bill when he is newly a ghost/wandering soul/ whatever the fuck he is after euclydia, but on the whole they're pretty laissez faire with him. Even more so after they betray him in some way and he makes a point to try and escape their oversight.

I think that the axolotl is the one who brought him to the nightmare realm. Sidenote--this also rests on another hc that bill's interactions with physics were never normal, which resulted in him being able to see higher dimensions and start fires with his mind. So, rather than rehoming bill to a similar 2d dimension where he would pose a further risk to himself or others, the axolotl took him somewhere that could accommodate his naturally unstable physics. They do see this as the best option for him, since he can function in the nightmare realm with freedom he didn't have in euclydia, but bill doesn't see it as a favor. When he asked for their help in the wake of euclydia, this is not what he meant. He wanted them to undo what he did, but they refused. As a god, i think the axolotl doesnt have the same conception of "good" and "bad" as a mortal might. Death is not inherently bad, its a part of the cycle of life, so they have no incentive to revive euclydia. Everything dies. In fact, it would be against the dimensional order of things and disrupt the harmonic flow of time to undo what bill did. technically, bill isn't even supposed to be alive to make the request.

In tbob, bill says he escaped to the nightmare realm and basically instantly became king, which is obviously a lie. His enthusiasm towards the place might also be put-on in the same way that he describes everyone in euclydia loving him and thinking he's the best. When he's in a situation he doesn't want to be in, he retroactively paints it over and makes it into a positive memory where he has agency. I wasn't stuck anywhere actually i chose it and i ruled that place, everyone loved me and no one treated me badly, i destroyed my dimension on purpose, etc.

Early into his stay in the nightmare realm, he maintains contact with the Axolotl, still trying to convince them , but they just encourage him to move on and make the most of his new fate, which he doesnt want to do. He still has a bit of faith in them, so when they tell him this is for the best he wants to believe it, because he has no one else to look to, and the axolotl is the closest thing he has to a tether to euclydia. They're the only other living being who remembers it.

But, then, he finds that the nightmare realm is dying, and he can't get out, and his opinion on the axolotl sours. They trapped him here and they tricked him into thinking it was a good thing, and now all he wants to do is one up them. He knows the axolotl keeps an eye on him, and so he acts out to provoke them and try to get them to initiate contact so he can chew them out to their face. Maybe he gets the confrontation he wants, but the axolotl doesnt take to the enemy role the way bill wants them to, they still care for him and they maintain theyre doing whats best for him, and theyre okay with bill being mad at them, but they arent going to retaliate. Or maybe they dont get a confrontation, and bill just has to live with the knowledge that he's under the constant watch of someone he hates (hey just like portal ford!), and that background awareness of their presence that used to feel like a comfort just unsettles him and makes him restless. Maybe he doesnt run into the axolotl for a very long time, and the next time they meet he's expecting a face off, but ax just says they'll help him if he ever needs it, which infuriates him, because he doesn't want their help.

It's important to note, if it wasnt already obvious, that the axolotl does care about bill. They have good intentions through and through. But they, like his parents, repeatedly end up hurting him in the process of trying to help him. Good intentions just aren't enough.

So, fastforward a few billion years, and bill finds earth and 46'\, makes it his mission to take over and gtfo the nightmare realm, and in the back of his mind he's always thinking this will show that bastard salamander for trying to keep him trapped, for letting his dimension die. They cant stop him!! And...they dont. Weirdmageddon happens without their intervention, likely because they have clearer vision of the future than bill does. But also because of their weird god morals and their interest in letting fate run its course.

So, when bill dies, he has no one to turn to but the axolotl, and he knows they're a big softie and he can probably convince them to let him keep living. they're the one who offered their help, and, well, bill is not going to ask for help unless he has no other options, which he doesn't at the moment.

in his mind, he's not even asking for help so much as trying to sway/convince them. And when the axolotl agrees to give him a second chance, from bill's pov that's not because they care about him (because he refuses to believe that they do) it's because he did such a damn good job selling himself. and, coming straight from weirdmageddon and believing they were too weak to try and stop him, he thinks he can take advantage of them. sure they fucked him over before, but that was a long time ago, when he was way more naive than he is now. he sees them now for the big soft hearted idiot they are. all he has to do is pretend to be remorseful and they'll give him what he wants!

And then the axolotl sends him to theraprism, yet again trapping him in a dying dimension and leaving him worse off than before (fell for it again award). So in theraprism, Bill is fresh off a second betrayal and vengeful towards the axolotl all over again. he doesn't trust them, and he doesn't want to believe a word out of their mouth, which is ironic, because they only deal in truths.