I wouldn't read too much into that short scene with professor Burke. Remember, Jade was also there. I think it was some kind of party - Jill will say something later how both, Bella and she, like wine tasting. So, probably a group of friends/colleagues from college have some wine tasting evening.
It must have drama - that's the DPC's rule. Frankly, if there isn't drama with Jill then her character would be quite two-dimensional compared to other girls.
Again, my friend Pepe SIlvia noticed many interesting details regarding those two.
Jill is telling Bella how MC was harassed by jocks and she concludes:
Jill: Yeah, I couldn't help myself but to feel sorry for him.
Bella: Where you're coming from… I understand.
So, it's normal for Jill to feel sorry for someone being bullied? Maybe there was domestic violence in her family? Father beating mother or something... And I don't think they're just friends - they are related. It's even possible they're mother-daughter and Jill doesn't know that. Yeah, it sounds crazy but there is one really interesting scene after Jill's yoga.
MC: It’s not like she’s your daughter or anything. Let her make her own decisions.
(Bella looks on the right silently)
Bella: I know boys like you. You’re only after one thing.
You basically can't miss that moment when she stops eye-contact with MC. Is it possible Bella had Jill as a young underage teen? Moreover, if Bella is from a rich and respectable family, that would be seen as shameful. Maybe her parents would cover up that and would decide to raise Jill as their own daughter - telling her Bella is her older sister. That's something you could even find in RL.
