Well, if you were an American and the president walked in, you'd be expected to stand up, whether you voted for him or not, or thought he was a tosser or not.
Likewise, if you were in the services and an officer walked in, you'd be expected to stand and salute. You'd be saluting the office not the person.
If you consider yourself a 'citizen of the world' rather than British then don't bow. If you have republican sentiments and you want to make a point of it, then don't bow. If you're proud to be British and you're not a republican, then bow.