Reggae is supposed to have groove. That is the most important aspect taht a bass player has to have in mind in this style of music. Without that, you ain't got nuthin'. Secondly, although the drummer and the rest of the rhythm section is likely to base their music on the upbeat, you have to keep the music centered around the first and third beats. The bass player keeps the thrust of the music on these beats to give closure to the music. Remember to use rests often to add to the rhythm of your line!

Sorry about the drum track, I know its based on beats one and three as the axial rhythm, its just that that was all that was available.