For the situations you're playing in, I'd say you really don't need to break the bank. A well-made chinese hybrid bass with a carved top and laminate sides should run you something in the $2000-4000 range, and those work especially well for jazz, in my experience. I'd say check out the basses at
www.lemurmusic.com or even give them a call and ask for advice. They ship all over the place, and they do a lot of personal work on the instruments before sending them out. Their sunrise series sounds like it might be what you're looking for. Also they're just really really nice people.
Whatever you do, DON'T go buy a bass from a generic music store. Places that carry all sorts of instruments tend to not do a very good job with basses. You're best off buying from a place that specializes in basses and knows how to do good setups.
Edit: where are you located? people might be able to recommend some good places in your area.