Some bassists are actually very happy just playing alone. Especially if you are good enough to do some insane riffs, and well less riffs but real Jazz on bass you know. Also if you could learn fretless bass it gives more possibilites.
I was always of the camp that thought it was a bit dull to play alone, so I only really play as much as someone who can pick up most instruments and play them OK. And as a guitarrist of many years it helps.
As for guitar, I'd recommend it. I'm self taught, the only lessons I've had are from other guitarrists I've met who have helpful hints.
I find new skills and talents on it come from osmosis. When I come across something at the right time it just clicks. If it's not the right time, I won't pick it up.
After 10 years self taught (the earlier you start the better) I have played live, and am working on an album (after having recorded some stuff, and an album for a friend a couple of years back), so it can be done. I guess what it takes is the motivation, and since music is pretty much most of my life (the one thing I couldn't live without say) I have had a fair bit.
As for other instruments, well, guitar and bass are certainly easiest to self teach.
Plus, as Wombat said, tuning is going to be particularly hard if you are un-musical, let alone playing. My mate (a drummer) is learning at the moment, and it's not easy, since he just isn't grasping certain aspects.
If you can master harmonic tuning it's best becuase you get the best tuning possible, but it does take a good musical ear.
If not, an electronic tuner does do the job, unless you're going to play around with CGCGGE or even just dropping all the strings from EADGBE to a C tuning or such.