Does the bill of rights contain privacy rights?

Procedurally, yes. Substantively, no.

There are certain procedures that law enforcement officials must follow in order to not violate your "privacy." For example, they must have a warrant or sometimes, in exigent circumstances, probably cause at the site, before searching your home and/or your posessions without your permission.

There is no such a thing as a *substantive* right to privacy in the Bill of Rights. By that I mean that you do not have the right to do anything you want to do, claim that it's your right to do it, because it is your right to privacy to do anything that doesn't hurt anybody else.