I think you're right: Alice has established from the start that it's a professional relationship. Continuing to flirt with her is inappropriate. There's no work

I think you're right: Alice has established from the start that it's a professional relationship. Continuing to flirt with her is inappropriate. There's no work-life balance element to this: Bob's welcomed to try to get laid. But he should find someone else. Other fish in the sea. For better or worse, that's one of the trade-offs of being a "big wheel." You have to consider how your actions might affect a whole constellation of people around you.