While I don't think that Kill Bill necessarily lends itself to deep interpretations of any kind it is very much a movie comprised of homage after homage the implied relationship between Beatrix and O-Ren is still of interest to me, probably because it's only implied. To me it seems clear that they were at some point actually and genuinely friends, or at least, as close to friends as coldblooded assassins can get. You see a hint of camaraderie with Vernita, but not much, even though Vernita is much more personable than O-Ren. Vernita apologizes, but it seems equally clear to me that it's more driven by fear for her daughter. Once she ascertains Beatrix isn't going to kill her daughter, she goes for the kill, which is really just pragmatic.
From the moment Beatrix steps in the garden, her expression is hurt, as a contrast to the merciless slaughter just moments before. She is tired, but also fights wildly and without control at the beginning. O-Ren is (as we've seen in previous scenes) completely controlled and composed until Beatrix forces her to confront what she's done. Given the fact that O-Ren is, er, kind of emotionally disturbed and extremely cold, it seems like when she does finally apologize, it's the first time she's acknowledged (maybe even to herself) that what she did to Beatrix was terrible and unforgiveable. That they were friends, and that trying to kill Beatrix and (as far as Beatrix knows at that point) killing her unborn baby was, you know, a dick move. She apologizes specifically for ridiculing Beatrix (for ridiculing whatever past they had together, because clearly they both love and favor Japanese sword fighting), but it's obviously an apology for, well, everything. And Beatrix accepts it, but welp O-Ren you gotta die. She'll just be real sad about it for a few minutes, but that bed was made and that grave was dug and they both know it. It's unfortunate that O-Ren was a big ol' sociopath who apparently did not understand how deeply she hurt Beatrix until that point (LIKE... EMOTIONALLY, NOT JUST BEATING HER 90% TO DEATH), it's just not the biggest tragedy here, pretty sure that belongs to being beaten 90% to death and put in a coma for four years by someone you loved and someone you thought was a friend. I mean all this is very much surface interpretation? It's entirely from Beatrix practically being in fucking tears from second the fight in the snow garden starts, because it's really hard to judge what O-Ren feels from how she reacts to shit. Most of the time she doesn't react much at all, and I would guess that's because she's almost entirely a soulless killing machine or has worked really hard to be one. I think she was genuinely sorry, though. Perhaps only because she realized she was fucked, but no, really, I think somewhere, some tiny alien part of her was like "oh, yeah, I guess that was a shitty thing to do... :c" and okay, probably she added, "... and now everything I liked is dead/destroyed :C" but seriously, Beatrix made her recognize and acknowledge it at least a little. And I don't think there's anyone else on the planet that could've done that.
I really, really need to rework what I came up with for her backstory, because I came up with that a few years ago and it's always seemed unsatisfactory and patchwork to me. It contains parallels and references to Lady Snowblood, naturally, but I just don't like it anymore, it's not thoughtful enough. So this will be on the list of things I think about for whenever I get back into RPing again.