What register to play in when improvising?

Got a good question from someone today:

What other instruments are the ideal instruments to accompany bass clarinet? Should a double bass and bass clarinet stay out of the way of each other? Would a cello be better? Does it matter what the other instruments are or can they clash because they are in the same octave space?

If you play with a piano, would you try and play in different octaves, or close together for example?

Generally when two or three instruments play together, is this something that sets apart the good from the great? (So when the bass clarinetist comes to play, I know how to play...)

Only reason I ask is I've heard people say not to play bass lines on guitar when bass guitar is doing them etc.

So here's what I do: When playing in that kind of environment (small jazz combo) I usually play in the top two octaves. Here's an example:

Usually I never play in the bottom register when I'm improvising in this setting because, first of all it doesn't project as well, and secondly it does muddy the waters with the bass (and low toms and bass drum, and left hand of the piano.)

That said, I still do it sometimes, just judiciously. When that's the case, any good bass player will hear that and drop out.

Hope this helps!