Stretch your left hand before even picking up the bass. Begin by pulling each finger back for 5 to 10 seconds or until you begin to feel the stretch. Do not pull too hard, otherwise you will damage your tendons. After this, repeat the process by stretching all four fingers back at once with the palm of your right hand. Repeat the process, careful not to pull too hard, for at least 3 minutes. This will lend initial dexterity to your playing.
Begin on the low E string. Place your index finger on the fifth fret and then use each successive finger on the next fret--middle on the sixth, ring on the seventh, pinkie on the eighth. Pick or pluck the strings in a steady rhythm, alternating up and down, as you go. When you reach the eighth fret, place your index finger on the fifth fret of the A string and repeat all the way up the body of the neck, picking along the way. When you reach the eighth fret of the G string, begin again with your finger on the fourth fret of the E string. Continue until you reach the head stock. This will both give you left hand valuable exercise, as well as increase the rhythmic consistency of your picking or plucking.
Pick or pluck each successive note in this exercise. Begin with your middle finger on the sixth fret of low E string. Next, use your index finger to play the major third on the fifth fret of the A string. With your pinkie play the eighth fret of the E string. Then play its major seventh by placing your ring finger on the seventh fret of the A string. Repeat this process up the strings. When you reach the top, invert the order back down. Then begin again with your index finger on the fifth fret of the E string. This will sufficiently give each finger on your left hand strength and dexterity for playing up the neck. As the frets get larger towards the headstock your hand will become more tired, but will gain much more strength.