Stay professional.
If you don't have to meet with the person face to face, don't. Write things down and give that to them.
Flat out tell them your impression. It's possible they have no idea they are being rude. Doubtful, but possible. You have to inform this person there is a problem though.
Document. Document what this person has done. Document that you have actively tried to remedy things yourself first -- ie You aren't just complaining. You have tried to find a solution to the problem yourself before involving anyone other then you and this person.
If you communicate in writing, they will probably respond in writing. That's instant documentation. Email works great for that. If this person is being rude in writing, you've got it documented.
After you've informed the person who is rude, and if they are still rude, go to the person right above them. Follow the chain of command. Don't go over the rude person's head until you have talked to the rude person though -- Otherwise the higher up person will be wondering why you are just complaining and didn't try to solve the problem yourself first.
Be professional. Be assertive, but not agressive. Don't ignore it if it is a problem.
I wouldn't worry about where you document this stuff. As long as you're professional about it -- It shouldn't matter who reads it. If your place of employment spies in and reads your email, then they get to read your list of documentation about an incident.
Make sure your totally blameless too. If this person has a problem with you, they may be making their own list of things you're doing wrong. Don't do anything unprofessional at all. Give them nothing to complain about.
Make sure you do something. If you do nothing, someone could said you ignored a problem and allowed it to continue. You don't create a problem, but you can definitely get blamed for one. It's no fair, but I see it happen.
Check yourself. Try to see if you're doing anything to create the situation. Hard to do but it's possible you do something to contribute or encourage it. (I doubt that though.)
When you document things, it has to be objective. Use exact words. Use specific numbers -- count things. It makes a difference if something happens once, or if it happens ten times a day everyday for three weeks. When you document stuff over time, you'll be able to see patterns. You can show that some type of behavior is consistent -- So if you don't deal with the issue, you have enough of a track record to be able to predict the future, and that's the future you don't want, so you must deal with the issue.
You can only document the stuff that the rude person does directly to you. You can't really be sure of a rumor -- No one will believe that. Focus on how this person interacts with you. If you use another person as documentation, leave out their name. It would have an impact to say that five people have heard this person make a certain comment about you. If you go to someone higher up or this rude person themself, leave the names out of the other people since you don't want to drag them into an argument.
Since it's your boss, that makes it much trickier of course. I would consider leaving if that's an option. There are always other jobs out there. The person you work for is going to have some impact (possibly) on your future -- Can you really use them as a professional reference in the future? If you do leave, stay professional -- You don't want this current boss to be a thorn in your side in the future. Give them nothing to complain about if a future employer contacts them while making hiring decisions. If you're leaving this boss and you've got some documentation, you've got something more solid if anyone in the future asks what the problem was at your current job -- Not that that will do much good, but being able to say "My boss didn't keep me informed. I missed seven meetings because this boss didn't inform me about them, and informing me of meetings is part of his job," that's better than just saying "I don't like my boss."
Specific, measureable, objective documentation is hard to argue with.
IF, and that's a big IF, IF all the documentation is worth it. You may come out of the situation looking bad, even if you're not at fault. You can do something. You can do nothing and put up with it. Or, you can leave. That's usually about the only options.
If you're speaking to this person and they say something rude, tell them. Let them finish their sentence. Then repeat what they said, and then tell them you find it rude -- "You said 'blah, blah, blah,' just now right? (They will have to agree because they just said it) I find that rude." And leave it at that for them to respond. Or add, "Don't you think telling someone... blah, blah, blah... is a little rude?"
I tend to avoid these people, but that doesn't always come out so well. Sometimes, it really makes me look bad. At the least, it creates a negative influence on things. Things don't happen that might have. Things aren't thought of that might have been. You don't add those extra touches to projects that you might have. And that's a lose-lose situation for everyone. Which means... I would deal with the problem for your own gains, for your own best interest. Dealing with a problem head on also gives you more control, or at least the feeling of control, over the situation. So, if I had a problem with someone (and I do, can you tell?) I remove myself from the situation for a bit, regroup, get some hard documentation, and then confront them. It's possible to do this in a way that makes you look very professional and puts you in a good light. Ultimately, if you can resolve the situation and the other party is happy, then it's a win-win situation, but it's very tempting (and possible) to make the other party look pretty foolish. If the other person truly has done things wrong, you can be in a position to make them look bad, to expose them, if you want to play that card.
Avoiding a person is ok, but it cuts off communication. Clear, open communication is a good thing. I get "ghosts" in my mind and start putting thoughts in the other person's head. If you talk to them, you can find out what they're thinking. And -- you still have to do your job with this person, so you'll have to do some communicating.
It can be a tricky, stressful situation. Good luck.
And let us know how it turns out. I want more advice in this area too.
Once you've done all you can, you've done your part. If the person continues to be rude, just keep documenting and keep the higher ups informed now and then. That's about all you can do. Except leaving at that point -- Why didn't those higher up people help you deal with the problem at that point?