I recently had a new gas furnace installed (Carrier 58CVA090 Variable Speed Gas Furnace) and at that time the installers replaced the old exhaust vent with B Vent (this is the term they used). They also ran the exhaust from the gas hot water heater into this same vent. The vent goes thorough a brick wall into an exiting flue in a brick chimney.

At the time the basement was unfinished. However, I am planning on finishing most of it over this winter -- and I realized today that my current design has framing for a bathroom right up against the vent line... probably within 6 inches. It suddenly dawned on me that this could be a problem. Haha. I know I'm a little slow.

Are there any codes (or failing that, some guidelines) for how close framing can be to B Vent? If this is a problem, is the preferred solution it re-design my bathroom or can I have a different type of material used for the vent (or this section of the vent)?

If you can, look on the vent for the manufacturer, then look up the specs on their website. American Vent, for example offers a 1" clearance, which is pretty much the industry standard. Be that as it may, find out who makes your vent and check directly with them. If you can't get any help there, perhaps you can call the installer and ask them.
Good Luck

1 inch from any combustible material.

You can buy ''thimbles''. They are just a larger pipe with plates on the end. You install it over the B vent and then build the wall up to it. That maintains you 1''.