Difficult to say without hearing what's on offer...
But I find runs and widdles involving diminished second and diminished fifth work well in many situations ( see Phrygian and Locrian modes).
And octaves work in everything from disco to punk, perhaps with fifth to make a chord. Talking of which, a chord higher up with root, major third and diminished seventh works well in many situations as a sort of jagged punctuation...
Also recommend the Jonas Hellborg chord book - I found I couldn't reach half of them but the notes contained in 'em inspired lots of bass lines.