I'm old school and believe chord tones are what we should spend our time on. OK, that out of the way. If you want to expand on R-5 Ed's book on Building Walking Bass Lines will give you plenty of things to add plus open a few doors.
Read some bass clef sheet music. See what others are doing.
If you are not doing chormatic runs now -- playing the ole basic R-5 and then using chromatic runs to the next chord can be a way of expanding your bass lines. Chromatic runs are as simple as targeting the next root note - then miss it by 3 frets - then walk to the root one fret per beat and be on it for the chord change. Leaving early and being on it for the chord change takes one evening's practice, i.e. not a step for a stepper, give that a try.
Little theory on how to harmonize a melody line - what notes should/could be in your bass line may help.
Simple Melody Harmonization (Keyboard Tut. #8) - YouTube
Here is a list of notes that can, with a little help from your major scale box be put into "generic bass lines". See a major chord and know R-3-5-8 will work. See a minor chord and know R-b3-5-8 will work. Or R-b3-5-b7 could add a little something for the m7 chord.
Code:
Major Scale Box.
G|---2---|-------|---3---|---4---| 1st string
D|---6---|-------|---7---|---8---|
A|---3---|---4---|-------|---5---|
E|-------|---R---|-------|---2---|4th string
Generic Notes.
- The root, five and eight are generic and fit most any chord. Remember the diminished has a flatted 5.
- The 3 is generic to all major chords. See a major chord R-3-5-8 is a generic bass line that will work.
- The b3 is generic to all minor chords. See a minor chord R-b3-5-8 is a generic bass line that will work.
- The 7 is generic to all maj7 chords. R-3-5-7.
- The b7 is generic to all dominant seventh and minor seventh chords. R-3-5-b7 or R-b3-5-b7.
- The 6 is neutral and adds color, help yourself to 6’s. I like R-3-5-6 for major chords. Has a great sound.
- The 2 and 4 make good passing notes. Don’t linger on them or stop on them, keep them passing.
- In making your bass line help yourself to those notes, just use them correctly.
- Remember roots, fives, eights and the correct 3 and/or 7 will play a lot of bass.
- Get some of these generic bass lines into muscle memory.
Now the root may be enough, if you need more add a 5, if you can handle more, with out the music going off and leaving you, think of the above notes and how they could become part of your bass line. The song itself will dictate how full you make your bass line.
http://www.youtube.com/watch?v=g35zS1tVO3o Sounds like some generic bass lines to me.
Have fun.