Since jazz is a highly rhythmic music, the bass player's relationship with the drummer is very important. Thus the bassist, like the drummer, is required to make a short, staccato sound that emphasises the beat. So jazz bassists use a 'pizzicato' technique most of the time, rhythmically plucking the strings of the instrument with their right hand.
Larry Bartley demonstrates pizzicato playing, and the famous 'walking bass' sound that has been a feature of jazz and swing since the 1930s.