The bass player can't make a boogie woogie sound right all by himself. Without a piano, your drummer and rhythm guitarist must know what to do.
Analyze what a pianist's left hand does in playing boogie woogie. His pinkie is playing the quarter note downbeats, four to the bar. His middle, index, and thumb (some or all) are playing chords, partial chords, or simply an octave to the pinkie note,
on the 8th-note upbeats. The bass is the pinkie and the rhythm guitar (upstrokes) is the rest of the fingers.
In the 1970s, my band was playing quite a bit of Western swing. Our drummer - who was very good - had been playing the jump tunes in the "classic" way of swing drummers - ride on hi-hat or ride cymbal. One night we opened for Asleep at the Wheel, and our drummer saw that their drummer was playing these tunes quite differently: Same as what I described above for the pianist's left hand,
all on the snare (of course he kept the kick and hi-hat stomps going too). Right hand plays the quarter notes and left hand plays the upbeats. Once he had learned to do this well, our jump tunes sounded much better. I've had a hard time getting other drummers to do this because it's out of the box that rock has built for itself, but it's the right way. Another advantage is that it makes accents and ornamentations easier for the drummer.
Last week I scored a jump-blues piece for a pianist, and it's a good example to show for what the left hand is doing:
