| Hi,
Mainly in Punk the Bass player plays just root notes E.g. Blink 182-All the Small Things. Of course if the Guitarist is playing power chords then it gives the Bass Player room extra room to be fancy.
Check out some Bass Lines by Matt Freeman (Rancid, Operation Ivy). He occasionally uses Walking basslines which, although not as extreme as Jazz ones, spice up the songs. | 
