Since this thread is a sticky, I'll chime in. I'm a classically trained pianist, but decided some time ago that I really dug the bass. I never did take that step to playing guitar. Most piano players are taught the instrument as a solo instrument, which in many contexts, makes us pretty good musicians. However, it can also make us quite arrogant. Young piano players are held by lay society and musical society as "the best" which can create quite a complex in a collaborative setting. We can run over chords, add weird dissonant accidentals (cool when your solo, not so much in a straight ahead blues/funk/soul setting), and (can) assume that the band/ensemble/quartet/etc. is our band/ensemble/quartet/etc. But this can all be trained out. It takes some time, but if the keys player honestly wants to be part of a collaborative musical effort, he'll change his style accordingly.
As far as a pianist being a "busy" player, if it's just during solos it's probably fine as long as his solos are in rhythm, in the right key (which might be obvious, but you'd be surprised...), resolve themselves in a timely manner, and generally fit the sound of the rest of the band. If he/she is running all over everyone in the band all the time, then this needs to be remedied.
A good keys player can add so much fullness to a band and really round it out. But "good" here doesn't mean simply theoretically and technically competent, it means an ability to adapt to the band's sound, change their style accordingly, and, yes, take criticism every once in a while.
How to broach the subject? Be kind (we tend to be a sensitive bunch) and just let him know that what he's doing is screwing with your guys' sound and not allowing you to do your job as a bassist. If he's got the technical chops, then let him know that, but don't kiss his ass. If his technique is weak, praise his sound.
The bottom line is that any kind of musical ensemble is a complicated relationship. Each member has their roles and ought to have a common vision. If a keys player is unwilling to compromise, play his role, and see the vision then it's time to find a new keys player.