The fun part of being a bass player, to me, is to be able to influence the music in a more subtle way. I mean, a drummer or a guitarist can do something flashy or over-the-top and get noticed, but as a bass player you can get away with things since you're "flying under the radar". And that in itself is a nice challenge. You'll rarely get standing ovations after the gig, because to the people watching, the drumsolo or guitar spot is what stood out. But from the guys in the band, you'll get quiet appreciation because they know how much your holding things together means.
Not that guitarists or drummers have to be that way. It's kind of a stereotype. But in general, bass offers people, who are not necessarily very concerned about being front and center, the opportunity to do some cool stuff in the background. Stuff that makes the music so much better without it being very obvious.
Plus, it's nice to be the one who makes the floor and walls rumble...