One of the main preoccupations of bass players is how to develop finger speed by strengthening their individual fingers first. The dirty little secret is that everybody already possesses more than enough strength in their fingers to play fast. Think about this for a second- the fingers of an infant are strong enough to support their own body weight when gripping for support. People take it for granted that by strengthening their fingers will gradually increase their agility and work towards developing greater finger speed.
The problem of playing faster does not lie in individual finger strength, but rather the skillfulness of the mind- you have to be able to think fast! This means that the timeline between the perception of a musical idea and the transition of that idea into the hands is only successful because the fingers are following the orders of the central nervous system. Any noncompliance that comes from the fingers is a result of poor communication from the mind.
Along with applying the proper hand positioning for both the left and right hands, learning to use diverse rhythmic variations when practicing arpeggios and scales is an excellent means to start training the mind to think faster.
Practice this by playing a Lydian mode in diatonic 3rds up and down your fingerboard. Because the diatonic 3rds are grouped together as 2-notes, most people will only ever practice this as 8th notes or 16ths as these rhythmic subdivisions are multiples of two. To change the predictability of such a line and help to increase the speed of transmission in your mind, practice playing the same pattern in triplets.
Notice in the exercises above we are playing ascending 3rds both ascending and descending down the fingerboard. Once you get that down you could take this concept further and practice the same exercise descending, ascending/descending or descending/ascending.
If you are unsure of the proper left and right hand technique principles then make sure to watch the videos explaining that:
Anatomy of the Left Hand: Click & Watch Now
The Right Stuff: Click & Watch Now
If you are having trouble playing the exercise with all four fingers of the left hand make sure that your hand is in a palm up position curling the fingers into position so that each finger is in an alignment with the fret it is going to press. Make sure that the wrist is as straight as possible so that muscles in the forearm are used fully. This will ensure that the energy applied from the muscles of the forearm will be transferred directly to the notes you are playing. This will allow all of the fingers to be equal and strong enough for effective bass playing.
All the Bass!