Along the lines of a stick, I'd say the piano is closely associated (in terms of playing bass and lead at the same time). However, if you're geared toward a guitar or bass, I say go for either, regardless of how many more guitarists there are out there than bassists. Playing music is a wonderful thing, and although you have already mentioned the scarce time you have to practice, you might find yourself so passionate about it that you end up finding more and more time for it. Just ask what happened to me during high school, and how my grades went down after I got more into guitar
Good luck with everything, and I hope you have a great time with whatever you choose.