... happens after this:

Bella was trying to help him regain consciousness and that detail did change things for me. And the way he, now conscious, says this...

Bellatrix is a high-ranking female member of a male-dominated organization within an incredibly patriarchal society. Even though Bella absolutely has the skills to deserve the rank as Voldemort’s second-in-command, there are going to be sexist rumours about who she fucked to get there.

Voldemort trusts her like no one else in his service. This guy gives her a Horcrux to guard, unlike Lucius who gets the throw-away diary to use as a weapon during a time period where Voldemort was expecting to be able to make another one. He literally gives Bellatrix a piece of his soul and asks her to protect it with her life. That is a level of trust that would have likely leaked out into other aspects of his interactions with her, and people would have e noticed.

Bellatrix was close enough to Voldemort to know enough details about the prophecy to be aware of alternative candidates for the child in question. She also likely knew that Voldemort had a method of maintaining his immortality, even if she wasn’t totally aware of the specifics of the Horcruxes themselves. She is very public about the fact that she and Voldemort have private conversations where he speaks to her about things that he doesn’t tell other members of his Death Eaters, and is visibly surprised to learn that he spoke to Snape about some of the things he told her— and I don’t think that that shock is completely unwarranted.

He personally tutored Bellatrix when she was younger and just starting off in his army. We have no indication that Voldemort did this for anyone else. At best, public perception would be that he’s giving Bellatrix more attention than he is any other of his Death Eaters. At worst, he’s spending long periods of time alone with her in a society that thinks that a man and a woman being close is indicative of them fucking.

Bellatrix very obviously desires him, both emotionally and carnally, and makes no effort to hide this in public, even in front of her own husband who is saying nothing about his wife’s behaviour. She is also getting away with it in a society where a woman’s sexuality (and especially, a pureblood woman’s sexuality) is heavily controlled and within a organization that is specifically dedicated to upholding and enforcing that highly-controlling societal structure. Anyone watching this would likely have an opinion on the matter, and probably believe that something was going on between Bella and Voldemort and that Rodolphus was either benefitting somehow from the arrangement or was in a position where speaking up was impossible.

Voldemort goes back to rescue her in ways that he just doesn’t with any other member of the Death Eaters, often to the point of leaving them behind to be captured while he singles her out for special treatment. He’s also so happy when she escapes Azkaban that his emotions leak out of his Occlumency shields and into Harry’s mind, which causes him to become uncontrollably hysterical. And when Bellatrix dies, he cries out in agony and probably would have gone into a berserker rage had Harry not chosen that moment to reveal himself. Clearly, Voldemort feels something very intense for Bellatrix and that feeling eclipses pretty much any other attachment he has in his life, so that’s probably going to leak out elsewhere into his everyday interactions with her as well— and someone’s going to notice that and make assumptions.

He calls her Bella. Yes, it’s her childhood nickname, but who else does Voldemort use a nickname for, especially on the regular and in front of other people? And not to mention that the nickname involves him basically calling her Beautiful. Seriously, what do you think the men observing their Lord calling his married female First Lieutenant Beautiful think is happening when he does that?

When Voldemort sets up his court at the Malfoy Manor during the war before moving abroad, Bellatrix holds the role as the Head of his Household, with her importance trumping even that of the family that the manor belongs to. Quite literally, Bellatrix has taken the position of Voldemort’s First Lady— aka, the role that is normally filled by a man’s wife. She is also living in a place he has claimed as his home while being completely separated from her husband (as Rodolphus is not present at the Manor during the skirmish), and he even stays and lives with her after he returns home from his travels. And again, he does this while her husband is nowhere in sight and making no complaints regarding the fact that another man has stepped into his marriage.

I’m not one to consider Cursed Child part of my canon, but if you do then Bellatrix is quite literally the woman he chooses to carry his child. Whether they conceived Delphini the old fashion way or used some form magical IVF, Lord Voldemort thought so highly of Bellatrix that he chose her to be the matriarch to all remaining Heirs of Slytherin to come henceforth, all while cuckholding one of the last remaining sons of the Ancient and Noble House of Lestrange and getting away with it within a society where this would be seen as a betrayal of all they were fighting towards. Had Voldemort won, history would likely remember Bellatrix Lestrange as his wife simply because she was the chosen mother of his progeny, regardless of the fact that she was actually married to Rodolphus at the time.

Not to mention that all of the above is happening in a society that usually treats mixed-gender friend groups as something inherently sexual, given the reactions that we can see to Harry and Hermione’s friendship. A lot of people think that they’re dating simply because they frequently share the same air: Ron, Cho, Molly, Snape, Draco, Pansy, and a good chunk of Slytherin all think that they’re dating. There’s enough evidence to speculate that Ginny probably thought they liked each other prior to the beginning of Book 4. Viktor thought that they’re a thing while he was dating Hermione. And that’s because, just like Bellatrix and Voldemort, Harry and Hermione are close in a way that most men and women just aren’t within wizarding society. Generally, boys seem to form friendships groups with other boys, and girls with other girls; if we look amongst the crowds at Hogwarts, we rarely see mixed-gendered friend groups unless a romance of some kind is involved and that’s why people are quick to think that Harry and Hermione might be a thing. Place that same logic onto Bellatrix and Voldemort’s interactions, and you are absolutely going to have a lot of people thinking that they’re together.

So even if they’re not, public perception of Bellatrix would be that she’s the Dark Lord’s mistress. It’s probably not spoken of openly and only whispered in hushed conversations that the gossipers hope isn’t going to get back to either Bella’s or Voldemort’s ears, but the Death Eaters absolutely believe that they’re are fucking, and that Bellatrix is not only having an affair but that Voldemort is stepping in on a pureblood marriage with absolutely zero consequence. He is demanding that his followers treat her as his wife in all but name, and then goes about treating her as his wife in all but name through his interactions with her. So again, even if they’re not, there is definitely a lot of people who think that Voldemort and Bellatrix are fucking simply because they act like they are within a society that would take even one of the above points as concrete proof that she’s his mistress, let alone all of them in combination.