Many players and teachers mention the need for stretching and/or strengthening exercises.
Exercises may prevent problems - or create them.
It is a big risk to start an exercise program without proper knowledge of possible effects. Be warned for the culture of ‘building chops’ and for unmonitored exercise with hand grips. You are not supposed to use any kind of real force to fret the strings. The little force you might need comes from the strong muscles of the shoulder, to add some traction to the left arm and to move the right hand up and down the strings. . A focus on strengthening tendons and muscles is unnecessary and may lead to loss of dexterity and to strain injuries. A better option is to use lighter strings in the beginning and step up to heavier gauges later. Again, using elbow traction as explained here is to be highly preferred above squeezing.
Very important is the notion that most skeleton muscles are in a delicate balance to take care of flexing and extending our joints. Strengthening the muscles for flexing (agonists) and not their counterparts (antagonists) may disturb that balance and lead to injuries. Furthermore, the body should be considered as a unity. Doing arms, hands and fingers exercises while ignoring neck and shoulders or overall fitness may even worsen your condition for playing.
Overall condition is the basis for any special training. Persons with overweight and lack of general exercise are far more vulnerable to strain injuries. A wide variety of general exercises is found here. Running certainly is not the only activity to improve your condition and stamina. Relaxed swimming can hardly be overrated, because it benefits the shoulder and arm muscles that do most of the job when we play bass. Ordinary walking is great also. If you make it a habit to park your car at a 20 minutes walking distance from work, you will be covering most of what you need in terms of daily exercise.
Some specific exercises for bass guitar players are found here. These exercises will help to prevent both carpal tunnel syndrome and lateral elbow tendonitis, also known as tennis elbow. More hand exercises are found here. Of these exercises, nr. 6 might well be the single most important exercise for bass players. It stretches the inside forearm muscles to compensate for their repetitive contraction during play. Perform it three times before play, once or twice during breaks and again three times after playing. Make sure that you keep the hand palms together, but do not press. Try to relax your arms as much as possible. If you already experience stiffness, the exercise from the video where the guy keeps his hand against the tree might be helpful.
Take notice of the fact that stretches are never to be performed shockwise. Doing so may cause you to rupture tendons. Stretches should also be relatively mild. Fanaticism when stretching is dangerous.
If you stretch corretly, you will feel some resistance at first. After a few seconds, your muscles will relax in their stretched position. At that moment let go off the stretch slowly and easily.
Some of us start playing the bass guitar at a later age, just like I did. It may take them more time to develop finger dexterity. The following exercises may help.