Reading Ilya as having suspicions of Shane being either specifically gay or specifically bi is almost a separate question in my mind compared to what I see happening in the tuna melt scene. There's a mindset in certain male homosocial environments where you can be young, horny, get up to whatever with your equally young and horny pals, fool around, tell yourself you're just "blowing off steam" or whatever, and the fact that you will grow up and settle down with a woman will still remain unquestioned. This mindset considers any homosexual experiences in these environments as irrelevant, meaningless, in an entirely separate category than pursuing a woman to date, marry, etc.
What Ilya is volunteering here when he says, "I like girls, but I also like you," is the idea of putting what he has with Shane on the same level as what he might have, in a fully societally-sanctioned way, with a woman. The question isn't really about whether or not Shane likes girls -- it's about whether Shane can acknowledge that he likes men and/or Ilya the same way he might like (might be expected to like, expects himself to like) girls.
Why would Ilya care whether Shane is gay vs. bi? He doesn't. He wants to know what Shane is perhaps getting up to with girls, if anything, presumably in private since he hasn't heard of anything, so he can gauge where their thing ranks in Shane's life, if Shane is even consciously ranking it at all. He's probing whether Shane is interested in/capable of seeing what they have as a relationship, as anything other than "a bad idea."
And Ilya is precisely right to probe this, because Shane isn't acknowledging it to himself yet! Shane is so utterly drawn to Ilya, yet his internal self-talk is still completely about how he shouldn't be doing this, can't keep doing this, he keeps going back to him because his resolve is weak, he'll end it next time, etc. etc. He absolutely refuses to entertain an image of himself as a queer man who is simply and normally and mutually attracted to Ilya, which means he is deluding himself out of the context he needs to interpret Ilya's overtures here.
Ilya begins by describing his relationship with Svetlana as long-standing and intimate both sexually and personally but ultimately not romantic and, more importantly, not threatening to what he might feel towards certain other people who may or may not be sitting on his sofa eating a tuna melt. I mean, for all Ilya knows, Shane might have turned this around and said, "well sure, of course, that sounds the same as what we're doing: we're old friends now who fuck regularly because it's convenient but it's not more than that," and that would be an answer for Ilya. But that would require Shane to admit to himself that yes, he is regularly fucking a man in a way he enjoys and means to continue, and he's still so far from being able to do that! So instead, all Shane hears from Ilya is a locker room brag, just another element of their 'rivalry' where Ilya can beat him by pulling more women than he ever could or wanted to.
And when Ilya offers, "I like girls, but I also like you," what is Shane not able to say in response to Ilya offering that he likes both girls and Shane? That he likes Ilya back. He can lie that he likes women, 'of course' he likes women, but silence re: liking men/Ilya. He has not reckoned with his attraction to men/Ilya in relation to his self-perception at all, and that is why Ilya is asking, what Ilya is nudging him to do, in the most relaxed, comforting, safe environment that Ilya could think of to create for them. The phone call bails Shane out, and he's able to bring things back around to more "meaningless" sex without fielding any more personal questions that he can't answer. But obviously the sex is not meaningless and when Ilya slips up and uses Shane's first name and Shane responds in kind, Shane is confronted with the idea that what they're doing isn't some kind of "blowing off steam" mutually meaningless whatever thing, that that's not how Ilya has been viewing it, so he panics. The idea that Ilya has been pursuing sex with Shane while actively conceiving of himself (and almost certainly, by extension, Shane) as a queer man, and now might even be trying to pursue something more with him, throws water on all Shane's self-delusions.
From Ilya's perspective, Shane's response is devastating. Ilya may as well have fallen for a straight guy, for all that Shane is available to him, for all that Shane is able to acknowledge his queerness to anyone at this point, including himself. Shane publicly dating Rose is the final nail in the coffin -- Ilya has clearly spooked him so badly by trying to talk about their relationship in any terms other than "a bad idea" that Shane had to get a celebrity girlfriend to push their hookups back into meaninglessness.
It's not until Shane tries and fails at dating Rose and she sorts him out that Shane can come back to Ilya, self-delusions discarded, and answer all these questions honestly: I actually don't like women that way, I think I'm gay, yes completely, I do like you, I can't keep pretending I don't.
