Jason has had many parents Catherine and Willis Todd both in their own way bad parents. One worse than the other . He loved Catherine but she wasn't a good mom. And the less said about Sheila the better.
Then there was Bruce who was so much better than Willis best dad he'd ever had. But that was before he died… after he came back he deliberately tried so hard to not think of Bruce as his dad. He knew that Bruce had changed and as their relationship started healing he still didn't think of his as his dad.
That Bruce died with little Jason and thinking of this Bruce as that Bruce, the Bruce that was his dad, felt the same as them treating him as the boy that died in that damn warehouse. So Bruce wasn't his dad anymore… but that's only cause he had a good dad.
He still needs a good mom and Bruce is trying to connect with him.
I imagine that Jason talks to Bruce one day in the batcave and tells him that he's not his dad anymore (maybe he says “you're not my dad and you never will be”) but all he means is that Bruce will now be his mother. But he doesn't explain that so Bruce is just heartbroken; sad that he's lost his son. But then Jason after more time (maybe in front of Tim and Damian) asks Bruce to pass him something “hey mom could you pass me that screwdriver I need to tighten this damn screw on my grapple “ and he says it casually and completely genuine.
And everyone's just staring at him like he's done something but Jason is completely oblivious but after a few seconds without looking he holds out a hand and flaps it “Mom?” and Bruce is connecting all the damn dots, he moves as fast as he can cause his son just asked him to do something.
Soon it spread through the whole family and one day on patrol Dick asks about it
Dick: Ok, I'm dying to know. Why the fuck are you calling Bruce mom??
Jason who's stuffing his face with tacos” whaf’ucyo’me’n
Dick disgusted: finish your fucking food, what I mean is like did Bruce do something are you playing a joke on him did he- I don't know - something
Jason swallowing:No? He didn't do anything, he's just mom.
Dick: Nah, cause what the fuck does that mean?
Jason panicking: ok ok wait! Ok relax. He's mom. wait! He was my dad cause my first one sucked so the second dad was good yea? But both my mom's, while I loved Catherine, weren't good Mom's. So third time's the charm right?
Bruce who was listening in, on the verge of tears: I love you Jason thank you for trusting me to be your mom.
Jason embarrassed, mumbling: shut up mom…. love you too