George S. Ledyard
Don't train with him... Don't sit down next to him, bow to the person on the other side of you if you get stuck next to him, basically act as if this person isn't there.
This seems like practical advice to me. I'm not an aikido expert, but I am a psychologist, so I tend to appreciate practical advice.
The one thing I'd add is that while you may not have any right to control who participates in the dojo, you certainly have the right to express yourself and to vote with your feet. If you have serious concerns about this other person, and he's truly ruining your experience of aikido, then your sensei needs to know how you feel about it. I can imagine lots of reasons why sensei might not immediately act on your complaint. On the other hand, I can also imagine a lot of ways that sensei might respond to you in a way that suggests that he "hears" you, short of kicking the problem guy out. If you get no meaningful response at all and the problem continues unabated, then it's something to factor into your future assessment of the dojo.
I don't know any secrets about the essence of aiki. But adaptive coping in the rest of our lives involves both being able to tolerate occasional episodes of obnoxious behavior, but also being reasonably assertive and knowing when not to tolerate it as well.