MC is a party planner and responsible (or co-responsible) for guests list. On Bella's branch - MC invites her, Jill doesn't communicate with both of them (MC & Bella) for obvious reason and MC is able to easily admit to anybody that he invited her, except a few persons like Quinn and maybe Derek, according how he behaved in front of her. While when MC on another branch, then Jill invites her and MC recognizes her only during drinking game and asks who invited her in front of J&M and Sage.
When MC is not on Bella branch, Josy doesn't speak with Jill about Bella and how fun she is. Otherwise Bella tells Josy that Jill invited her (in front of all, including MC). Jill will never mention and talk about MC & Bella relationship to Josy. This may happen, if Josy will aware, especially if MC break up with throuple, and then she may ask Jill about Bella, because she know that they are friends. But it's a speculations, we can't predict how DPC will play out all this branches, break ups and their outcomes. While Jill is upset or even mad on Bella, she is not that type of person to get a revenge or whatever else in a way by making such delicate info a public state.
Yeah, and she covers Bella & MC ass at the best costume competition. I think she is one of a few persons whom will be ok to find out and accept the fact that MC & Bella in relationships.
We don't have any evidences that somebody recognized her. Only Quinn suspected something and was interested with mystic "mummy" too much. Even Derek hadn't recognized her.
Following this logic - each dance had to have consequences. J&M dancing with MC, and Tommy should show in no time, Jill dancing with MC - Sage should knew that since there a lot of dormies, which know Jill, even if Sage was in another place. Dance with Sage looks as the safest option so far.
He was too drunk and blacked out at the end. He will remember something of course. But it's a secondary problem, since Nick seen her coming out of MC room. Derek fucked up a lot, telling her about his tricks during classes
Last time it happened when mansion was trashed, all DIKs was in place and sober. It wasn't a party or something similar. So, in such case you are getting great capability to notice something, to wait for something, etc. During the party... especially so huge, with a crowds of guests, when most of them in costumes, etc. It''s hard to remember something, to notice something, etc. But knowing about the "tradition" he asked her (and she was awared already, because she did the walk of shame before) to come out through the window. And Bella noticed, that this party is the only one, she is able to visit and participate in, because all people in costumes and she can hide her face and body. And she had doubt a lot - to come or not to come.
Relationships with Bella is the most problematic by a lot of means. It's her past, her husband, age gap, her work at B&R, Stephen, Quinn (if she will find out) and a lot of people around, which mostly will not happy with this.
But, tbh, any of MGs have their own troubles, too:
J&M - the throuple thing itself, J&M lesbian thing, Patrick, Tommy and maybe Quinn (if and when she will find out about it);
Jill - her family & all possible connections to MC family, Bianca, Tybalt;
Sage - her family (Stephan and Tybalt too), Quinn - in every sense.