Cappuccino,

The set-up of a bass is usually specified by measuring the distance between each string and the fingerboard at the end of the fingerboard nearest the bridge. It's different for each string. You can change this height slightly by changing the notch depth where the strings go over the bridge or by sanding the top of the bridge appropriately. Don't change the feet of the bridge which are shaped to fit the belly of the bass. Adjustable bridges have brass or aluminium screws in the legs to adjust the height.

Many players change the setup when playing classical (a high setup) and jazz (a low setup) or for arco and pizzicato.

There are lots of variables to take into account.
How high is the action at the nut. A very small change in the notch depth may give you a more acceptable action but be careful of creating buzz in lower positions.
Is the fingerboard chamfered. This allows a lower action overall but gives better clearance for the E-string to stop buzzing.
Does the fingerboard "dip". This is a curvature in the surface which makes the action more uniform along the length of the fingerboard.
What tension are the strings. Lower tension strings may make a high action more acceptable.
Is the fingerboard ebony. This makes a differnce to the pressure required to get decent tone and sustain.

Do you normally play in higher positions where the action is higher or do you use 1/2 and 1st position predominantly. How do you position your hand and thumb and what fingering do you use. It really is different to a bass guitar in order to get the pressure required.   

Happy to answer questions here on on PM.

Mitch