Doc,
I'll try to break down a simple explaination.
Arpeggios are the tonal center for scales. As it applies to bass, when you are "playing the root", you should know what chord is being played. If you know the chord than you can use any of those chord notes, which correspond to an arpeggio pattern to create your bass line. Add in a few chromatics to the arpeggio pattern and you may have yourself a monster solo.