That's why I kind of stood there and pondered how good I really am. If he has expectations of a player who makes a living playing bass and I told him "yes" then he'd think I was a liar after he found out I work in a factory.This individual is slightly misusing the english language. He is searching for a way to ask you how proficient you are. It's a hard question to answer because if he's already unclear on what "professional" means, it's probably going to be very hard to describe to him how professional you are.
Interestingly enough,one of the noun definitions ( http://www.websters-online-dictionary.org/definition/professional read the first set of definitions, not the wikipedia notations that follow) of professional is "an authority qualified to teach apprenticies" this might be a good way to reflect on your abilities. Are you good enough to properly teach apprentices?
If playing bass is your profession (i.e. you're making most of your livelyhood playing bass), and you are good enough to pass your skills on, then the best answer in your case is probably "yes".
In my case, I get paid to play, but it's not my livelyhood, so I would answer now. Also, I'm probably not a good enough bassist to be a good teacher of all but beginning students.
I can teach people up to a certain level and have on both guitar and bass but they were kids. I probably could teach an older bassist some things but then again he could probably teach me a few things too.

