Something I read in a jazz book years ago: imitate-assimilate-innovate. Imitate: in other words, steal liberally. You've probably done this in your drumming. Pick a song or riff that catches your ear. Slow it down and learn it exactly. Assimilate: analyze it and understand it (is it part of a scale-an arpeggio-a mode? what are they doing rhythmically, what register on the bass, vibrato etc). Innovate: once you have command of something you can use it at your discretion any time you want. Just like you can tell a closed from an open hi-hat and the sounds of different toms you'll start to see and hear all the things you are practicing appearing in the music you listen to. At that point you can play (create) whatever you hear or feel at the time. Hope this helps.
This is the biggest 'secret' to bass playing period. It seems simple but it takes time, work, and dedication to achieve the bass lines you hear in your head. Have fun and don't forget your ABC'S!
