Here’s a great video clip of Paul Baloche explaining what he’s looking for in a bass player.
In this clip Paul focuses almost exclusively on the bass player’s skill. More important than the bass player’s skill, of course, would be his or her heart. Do they love the Lord? Are they passionate about God’s glory or their own? Are they humble? Are they committed to the church? if these answers are “yes”, and the bass player is skillful (like Paul talks about), then sign him (or her) up!
Worthily Magnify 
Paul mentions something at the very end of the clip that I think is key.
As a drummer, I’m also hoping that the bass player I’m working with can stay in the pocket. Listen to what I’m doing with the bass drum. I’m not going crazy, I’m just laying down a groove. Try making your right-hand rhythm lock in with my bass drum pattern.
The bass player and the drummer are the “rhythm” section for a reason… we’re there to be felt. The more we lock in, the tighter the groove, and the less distracting we are.