OP, you do need to quit this job. But not for the reason you think. It has nothing to do with this scenario, but it has to do with you as a person. You are not cut out for being in the workforce. Please leave the workforce and do not return. Get married, find a spouse with a good job, who can baby you and coddle you and support you so you don't have to be around people, because you are not able to handle it.
If Bill wanted to be aggressive with you, he wouldn't have done it on Sue's screen. He would have sent you the message directly, and it would have been a lot worse than what he said. He did not "collaborate with Sue to try to haze you" or whatever; just as easily as you can take a chat record of the conversation and send it to HR, you could also take a screenshot of Sue's shared screen and send that to HR. There is no benefit to Bill for sharing his angry message with you via Sue, over just sharing it with you directly himself. This message was directed, if at anyone, then it was directed at Sue for keeping the meeting dragging too long, and you unfortunately saw it.
This is fairly ordinary when meetings drag over: Someone gets upset and sends a frustrated/irate/sarcastic message with someone who they are close with to express their frustration. The other person, because they are close, shrugs it off and doesn't say anything to management, as it would make them both look unprofessional if it got out. But it happens, at every workplace, at every time, in every meeting, and if not in the meeting then certainly after. I have almost never left a meeting in my life where nobody said "that meeting sucked I wasted my time" or something like that; there is always "that guy" in every meeting, and if you're going to be part of the workforce you need to appreciate that and deal with it. One of these days, you will probably be "that guy" yourself, if you haven't been already.
As for the laughing: It's embarrassing when these messages become public. Not saying these kinds of things is a measure of "being professional". What Bill said was not professional. The fact that Bill thought that Sue would not share the message was unprofessional, of Sue (for portraying that image). The fact that Bill sent the message to Sue despite Sue's screen being shared was unprofessional. The fact that Sue showed the message was unprofessional. But these things happen, mistakes happen, and usually you laugh them off and move on with your life, like "haha that was silly wasn't it, ok move on". Only the most uptight of uptight people even make a comment about it, and those are the people you absolutely don't want around, those people fail in office politics and are usually the first on the chopping block when downsizing happens.
As for the apology: Bill did not apologize for his comments. He apologized that his comments were made public. Because he has nothing to apologize for, to you. His comments were directed at Sue, not at you, and you happened to see them. His comments were not about you, they were about the meeting. He apologized because he did something unprofessional and you saw him doing something unprofessional, so he apologized to you for being unprofessional, and that's all. He did not apologize for "hazing" or "bullying" or whatever. He is not an "attacker".
What you should do: As above, you should leave the workforce immediately and never return. You are not cut out for being around people and working collaboratively. Your skin is much too thin to do that, and if you show people you have such a thin skin, and at the first indication of any sort of slight that may possibly even close to resemble something against you then you will launch a formal complaint with HR (seriously who does that?), you will never succeed because nobody will ever want to even be in your presence, nevermind collaborate with you on anything. So please, just fire yourself and don't come back.
What you should do if you decide you need money and can't just not work for the rest of your life: Get close to Bill. Bill knows what's going on. Bill seems like a cool guy who's not afraid to be unprofessional if it means he gets to be more sociable. Accept Bill's apology, go to HR and revoke your formal complaint immediately, and do your best to become friends with Bill. I would even go one step further: Find Bill's manager (in person, not by email, schedule a meeting if you have to), explain the situation to his manager, and apologize to Bill's manager for launching a complaint against Bill, and do it in Bill's presence. Revoked or not, a formal complaint could come up on an employee's annual review, and it could affect Bill getting a promotion or a raise when he did nothing wrong. You need to inform Bill's manager that the complaint was ill-founded, and you need Bill to know that you reported this to his manager so Bill can follow up if he needs. Then, you should accept that this is company culture in your company: Your coworkers are not robots who have to be mechanically professional all the time. They have personalities and they get frustrated or angry (or happy or excited) just like the rest of us, and sometimes they voice their opinions and their emotions, and everyone at the company accepts this and feels free and open to sharing as well. You need to accept this, not only at this company, but at every company, because every (good) company has this culture as well. Bill seems used to this sort of thing, so you should become friends with Bill and watch how Bill acts and emulate him, he'll be a good mentor for you not being hated by everyone in the future.