Funk is all about grooves and accents.
As the others have said above, you and the drummer must be totally locked in with each other.
And, again, as the others said above, the 1 is a very important accent in funk. I'd explain it like this: a big accent on the 1 and a slightly smaller accent on the 2 and 4. Most of the time people will expect to hear your drummer playing a big kick drum on the 1 and a snappy snare drum on the 2 and 4.
The fun thing about funk is that you, as a bass player, can throw in accents in places other than the 1, 2 and 4 to add some spice to the basic groove. This is why players like Bernard Edwards used a lot of 8th note syncopation (ie. playing the off-beats in 1 and 2 and 3 and 4 and) and players like Louis Johnson used a lot of 16th note syncopation (ie. playing the off-beats in 1 a and a 2 a and a 3 a and a 4 a and a). Don't worry about that for now.
To start off with, play the root note on the 1 and then pick your spot somewhere else for a few other notes. But as everyone has said, keep it simple. If it's cluttered, it won't groove.
As for who to listen to, there are basically two schools of funk: James Brown's school (which was in your face and all about the 1) and Sly Stone's school (which was more laid-back, making you clap on 2 and 4). As well as those two, listen to Parliament-Funkadelic, Curtis Mayfield, Stevie Wonder and Headhunters for a solid introduction to funk. You should check out 2nd, 3rd, 4th and 5th generation funk after you've checked out these guys.