Bass guitarists often use a technique of playing "riffs" against a chord progression. A riff is a pattern of notes that is repeated throughout a progression (or song).
The following two examples use all the notes within each chord, i.e., the 1st, 3rd and 5th notes of the Major scale relating to each chord. To play the notes of a chord one after another is often referred to as arpeggio playing.
You have probably heard this riff style of playing before. Play some records (fifties rock and roll or blues songs would be best) and listen to the bass.