Get onto YouTube, and search through the bass lessons, looking for left hand instruction.
You will see a lot of different players showing different ways to fret the fingerboard.
Also, as I go up the fretboard, I find I need to move my thumb towards the bottom of the neck (slightly) to access the higher notes. But I sling my basses low, which may explain that too
Finger stretching exercises are great, such as these:
G|-----------------|-----------------|-----------------|
D|-----------------|-----------------|-----------------|
A|-----------------|-----------------|-----------------|
E|-1-3-1-3-1-3-1-3|-1-4-1-4-1-4-1-4|-1-5-1-5-1-5-1-5|
The idea being to fret the 1st fret with your index finger and the 2nd with your middle finger, 3rd with your ring finger, and 4th with your pinky.
To start with you will need to skip your fingers, but the aim is to do it without skipping between fingers. Then move up to the next string and repeat.
Oh, and using a metronome with this exercise helps develop timing at the same time too! Saying the notes at the same time helps fretboard memorisation too, 3 birds with one stone and all that!
Hope this helps some.