As a bartender, if your brother said that to one of my coworkers and they were pissed I would have nicely asked him to leave. If he said it to me I probably would have told him to fuck himself and not worried about it.

The note is a good decent thing to leave but going directly to the lady your brother insulted and telling her that you are very sorry, your brother is a total asshole, you'll never bring him there again and you couldn't be more embarrassed to be related to him would make going to that bar again much easier.

Bartenders deal with assholes every day. Some will despise a whole party for the sins of one person, others understand that this kind of stuff is isolated to one individual. If it's a rough one I can shamefully be the kind of bartender that doesn't differentiate, but generally I'm ready separate the wheat from the chaff. That being said without a direct apology from one of you, I'd probably under-pour the both of you.

People have said some really hideous shit to me while tending bar and I've just let it slide by, hope this lady gets over it, she should have kicked his ass out.