You would ban bob's post from being shown on your instance's copy of the federated community.

This happened recently, where a prolific user on !noncredibledefence was instance banned on blahaj.zone. if you visited !noncredibledefence@shit.just.works from blahaj.zone, none of his posts would be shown, but they were otherwise visible on other instances. I suspect in the case you're talking about, it would only apply to the community on question and bob's posts in other communities would be unaffected.

Think of it this way. All bans and content removals are local only, and don't federate to other instances, with a few exceptions

The most notable of these exceptions are

i) a community moderator removing content or banning a user from their community. This federates. An instance admin doing the same thing does not federate, unless the community was created on their instance.

ii) an instance admin banning a user based on their instance, and choosing to remove all of their content. This will federate the ban and the content removal to other instances.