Certificate Authorities

What about Bob's private key?

Normally, Bob never reveals his private key to anyone (including the CA).  However, in some situations, Bob may be required to give it to the CA (or prove he has somehow put it in escrow).

What kind of key is this?
The usual situation is that Bob gets a certificate for his signing key.  He then uses his signing key to sign a copy of his public encryption key.
But even when you want to escrow private encryption keys (to recover encrypted documents), there's no good reason to escrow private signature keys.