The simple act of moving your elbow away from your side will straighten the wrist. Lowering the bass will help straighten the wrist also. Your arm has the ability to lead the hand and keep the wrist straight in normal movement. When you next play let you arm be the hinge that sets the hand to the bass not the wrist.
Now in doing this you have to learn to keep your shoulders down, in other words tension free. Many players make this mistake and then introduce a new problem, shoulder and back ache, so kepp it relaxed.
Use a mirror and see what relaxed (shoulders down) feels like and learn this feeling, it always creeps back in when you start so learn to recognise it.
As for you arm.. you say you rest it on the bass, now it will be more on the front of the bass, so gently hug the bass to you, a sort of friendly very gentle clamp to your body with the forearm, this will help keep your shoulders down.
I feel i should mention that this is for you and your situation. If it is your job that creates the problems then bass playing will highlight them.
See a medical pro and get to the bottom of this pain.
Look in the health sticky at the top of this form and start using some stretches and light exercises to counter the effects your work has on your hands and prepare them for playing..a warm up routine if you will.
I have the same routine that i have use for over 20 years, it takes about 10 mins here or there. Because i know it so well if any part of it feels wrong then i know playing bass will not feel right or be affected, and make allowences for that.
