Try placing your hand palm down on a table. Lift the index finger about an inch (or as much as possible without forcing or straining), hold for five seconds then let it down again. Repeat this exercise with each finger, one at a time.
The good thing about this exercise is that it can be done away from the bass.
With the bass, try following the instructions in the link below. Also be sure to warm up first with gentle stretches, even before you touch the bass. Search You Tube for "Hand Stretches for (Bass)Guitar".
I would NOT recommend trying to to the spider exercise at this stage. IMO it would be too much of a strain until your hand and fingers adapt to what is required of them to play the bass. Dont over do the exercises at one go, but do them on a regular basis. http://www.youtube.com/watch?v=IeRoQuXlj9w
Here is a link to a similar type thread. pinky strength. mine is incredibly weak and I need help / advice.