I'm going to post a few classic reggae basslines to try to illustrate a few concepts that were mentioned in this thread. I was going to scan in transcriptions that I'd already made, but that was scuppered by the demise of my home computer...
I usually transcribe the bass and drum part, to me they are interdependent parts of the rhythm track, but I'm yet to figure out how to get closed hihat symbols in Finale notepad, so I'll describe as best I can what the drums are doing.
Rather than giving the whole tune I'll give examples less than 7 bars long (I believe that's the cutoff point for copyright purposes)
Here's the main bassline from Fisherman by the Congos:
I originally thought this bassline was by Boris Gardiner of the Upsetters, but it turns out it was Geoffrey Chung, who was sitting in.
Note the dropping of the first beat in bars 1, 2 and 3. This is an example of the "one-drop" that was already mentioned. This gives the bass a characteristically laid-back feel.
In terms of note choice, the chord progression is essentially |Em |G |G |Em ||. (There are two passing chords played by the guitar in bars 1 and 3, that may be D7, but I'm not 100%sure...). We're sticking largely to roots, 3rds and 5ths here. The bassline plays off of the vocal melody, which is a feature of a lot of reggae basslines (although not universal, particularly when the rhythm track is recycled for a different song).
The drum part is fairly simple. The hihat plays even eighths throughout, with snare rimshot on beats two and four. The kick drum is played on each beat.
Please speak up if you spot any errors!