I am a bass player who likes to compose songs as well. It is quite fortunate that I also play the guitar and that I can find my way on keys, so that I can't ever be bored when I am in the studio. I usually take great care of the lyrics, because I feel a song is more than just a set of sounds, it also conveys a message.
I have been influenced by many artists, but when I ask who frequently return, people mostly mention Steely Dan, King Crimson, Weather Report, Duran Duran, Jimi Hendrix, Roxy Music, Tower of Power, Niacin, James Brown, Primus - how is that for a salad? That is not to say that I try to mimic them, the influences just sneak up on me when I am not paying attention.
I play in projects with other musicians as well when they need a bass player or a guitarist. These are mostly soul & funk based, but I can mostly find a way in rock, jazz and folk as well.