rick fielding talked about bass runs, some tips,imo you need to know what notes of the scale make up a simple major chord, they are 1 3 and 5, then add into your bass run note 2 of the scale and note 6, so for g major chord a good starting idea for a bass run is gabdeg, note 12356 of the g major scale,this can be applied to all major chords, c major would be cdegac, this is just a starting point, next think about occasionally adding the fourth of the scale, sometimes instead of or sometimes before and/ or after the third note of the scale, so if playing a g bass run this would be a c note, you just have to experiment with this by ear as to when it sounds right.
the other completely different alternative is to look at the blues scale.