Xjyuk

I recently sent an email to a professor asking him about an administrative problem I was having, but after I'd hit the send button, I realized I'd forgot to say: "Sorry to bother you" or something of that sort in the beginning...
Now I'm wondering is that considered impolite? Shoud you apologize to professors for bothering them or does that just make you sound phony? I greeted him with"Dear Professor X", told him who I was, asked the question, and thanked him in advance.
He answered my question and all, but I'm just asking for future reference.

I think that @ndpl hit the nail on the head when he commented that what's most important is that your message to the professor be clear and concise.

During an academic semester I, like most academics, get a crazy number of emails. (I'm an assistant professor of mathematics at a college in the US.) If your email is short and to the point then chances are I'll be able to read it right away, decide what action on my part needs to be taken (if any), and move on to the next email. Empty statements like "I'm sorry to bother you." are polite, but just make my goal of getting through all the unread messages in my inbox that much harder to achieve.

So if your email was written in a professional manner, but was just terse, that's absolutely fine.

Perhaps it's worth making one point clearer: certainly blathering pseudo-politenesses is silly and off-putting, BUT demonstrably knowing the currently-accepted forms of politenesses is itself a filter, which you'd want to pass.

That is, knowing what exactly to say that is currently considered polite and appropriately respectful for the situation, is in itself a filter, whether or not we think it has genuine meaning. But it is surely the case that knowing the current formulaic politenesses does a good bit in the way of getting one's foot in the door.

Actually-non-ironically, as people try to use internet resources to find out what the successful formulaic politenesses are, the criteria shift to compensate. E.g., all the discussion of "what makes a good X" is self-defeating, in sort of an inflationary way, in the sense that whatever the current formulaic answer is is a failure.

I'm not a professor, but as a professional who works in an office setting (and gets a lot of random requests for help from people I barely know), I'd say: it's probably good to get yourself out of the habit of using filler like "sorry to bother you". I personally find it disconcerting, as if people assume I'm some kind of ogre that is just as likely to chomp their head off as to help.

Certainly politeness and concision are important, but others have already highlighted this. Keep in mind too that your professor is aware that one day you will, hopefully, be their colleague/work-equal, and that as such, conducting yourself in a professional manner (which includes holding yourself in esteem) will be important.

Edit: my only experience is working within the United States, so this answer is intended only to apply there.