When playing in the upper positions on the bass, the thumb is employed to stop the strings just like the other fingers, and the third finger is used instead of the fourth finger.
When approaching thumb position while standing, you must take a small step back and rest the neck of the bass on your shoulder. This is not easy to do at first, and it can be very awkward, but with practice it can start to feel quite natural, as long as you do not tense up or shrug your shoulders. If seated, no special adjustment will be necessary.
While playing in thumb position, the elbow should be up enough so that the arm does not rest on the shoulder of the bass. It is fine if the arm occasionally touches the shoulder, but it should never rest on it.
The wrist should have a slight arch to it.
As you place the thumb on the string, it should be pointed to the right and fairly parallel with the nut and bridge. It should touch the string just in front of the joint on the side.
The other fingers should all be arched, but slightly more on the tips than in the lower positions.
There are three basic hand shapes used:
Chromatic: half step between each finger
Semi-Chromatic: whole step between the thumb and first finger, with half steps between the rest
Diatonic: whole steps between the thumb and first finger, and first and second fingers, with a half step between the second and third finger
Remember that the upper body should not feel tense at all. Do not shrug and be careful not to bend at the waist too much or tilt your head down excessively.