Watch the Start And Finish online guitar lesson by Jasper Mortier from 50 Blues Bass Licks You Must Know
Bass players in the 60-ies and 70-ies often constantly muted their strings with foam. But with this overall way of muting you just make all of the notes die out faster - which can already sound funky enough though! - but it the note doesn't stop at a specific moment. To be more aware of the length of the note try to think of 'organ' for instance since that's got an everlasting sustain as long as you keep on pressing the key. This way of playing also helps to be more aware of all of the 16th notes in your part and not only of the actual notes picked. You'll also become more aware of the silence in between your notes. Those are at least as powerful as the noise you're making!