You should read up on both
tendinitis and carpal tunnel. Tendons generally connect your muscles to your bones, and it's pretty typical to have
some small amount of tendon pain when asking muscles to do new things. The key to preventing this from becoming tendonitis is to cut back on the activity causing it, then begin a regime of light resistance training/stretching/strengthening (which can include some bass playing). Carpal tunnel is a nerve syndrome, I find it much more complicated to describe.
Here's a pretty cool picture of the muscles and tendons in your hand:
Carpal tunnel syndrome is when the bones or muscles compress the nerve that runs through the carpal tunnel into your hand. The symptoms of each condition are a bit different:
Here's some common doctor brochure language about prevention (of tendinitis):
Preventing wrist tendonitis is much easier than treating it. If you undertake activities that may put stress on the wrist you should always make sure you warm up the wrist area before beginning such activities. You can warm up your wrist by stretching and flexing it in various directions. Twisting the wrist 360 degrees slowly is also a good method.
(It's spelled both ways, tendonitis and tendinitis; my doctor spells it tendonitis but firefox spellchecker disagrees).
For a bass player, individual finger exercises are equally important as warm-up. There are quite a few websites with exercises and instructions for warm-up. Warming up helps with both CP and T, but if a person has the beginning symptoms of CP, bracing and immobilization
supervised by a competent hand specialist is crucial.
(That instruction about 360 degrees of twisting is sort of funny - obviously, they mean "as far as possible in one direction, then the other" not, in fact, twisting your hand off!) A combination of self-massage and stretching really really helps (I've been on the verge of repetitive motion syndromes several times over a few decades and have managed to avoid any longterm problems).