You should never feel tendinitis. It means you need to adjust your left hand technique, and the only way to do that is take some lessons from a pro. Here is the carpal tunnel:

If you put your put your righthand fingers on your left wrist (like you're checking your pulse) and wiggle your lefthand fingers, you can feel those babies moving in there. If you bend your wrist, you can feel the tension increase, like a rope rubbing against a ledge. Eventually it frays, and nature provided extremely sensitive nerves there to tell you to knock it off. I'm primarily an upright bassist and one of the first things we learned was how to "lock" your left thumb as a cantilever so you maintain a straight line from your elbow, through your wrist to your knuckles. The thumb is directly opposing the middle fingers on the neck.

Here's Stanley Clarke:

We had to practice using just enough finger pressure to sound the notes, without squeezing, by using the thumb for leverage, rather than squeezing the neck like a baseball bat. The technique is slightly different for electric (because your thumb points across the neck rather than lengthwise) but the principle is the same. By using leverage with your thumb as the balance point you can keep your wrist straight and keep squeezing to a minimum. Note the straight wrists in the following. Here's Jaco Pastorius:

Jimmy Johnson (w/Stanley Clarke)

Another example is the amazing Delano Mills:

I hope this helps. If you continue to feel tendinitis see a doctor.