I keep mine much further away than I do my guitar pickups. It depends on the output of the pickup, and the attack of the right hand. If he's heavy handed, back the pickup down to avoid the string smacking the pole pieces. I don't have my bass handy, but I'd say I have 1/4-3/8" between my strings and pickups.
I think mine are just screwed directly into the body with four screws actually through the pickup casing. I don't think you can ajust the height of them :/ But I've not tried...
Unless you've got some sort of bass design I've never seen, you can adjust them just fine, Nuntius.
And RnR, just like with guitar, there is no set exact answer for this question. Tell you bass player to move'em up and down until it sounds good to him.
yeah...it just depends on his style...if he does alot of slapping...i find a little higher string action works, but guys who use a pick often like the lowest action they can get...i'm somewhere in between!
when i do play bass, i usually use a lot of slap.. usually pickup height is a case of getting it to the point where it dosen't get in the way of the strings or your popping fingers hehe