I have just had a new Payne furnace installed and have been told that the b vent needs replacing. Does that b-vent need to be for my hot water heater as well as my furnace? How much is the average cost of getting a b vent installed by a professional, this b vent will vent the furnace in the basement to the roof of a single floor family dwelling/residence.

I have just had a new Payne furnace installed and have been told that the b vent needs replacing

OK so replace it

Does that b-vent need to be for my hot water heater as well as my furnace?

That depends upon weather you have a clerance to combustible problem or if the B vent is enclosed in a chase.

How much is the average cost of getting a b vent installed by a professional, this b vent will vent the furnace in the basement to the roof of a single floor family dwelling/residence.

All prices are set by local labor rate and the cost mark up on the material. Get at least two local estimates to be sure of fair pricing. Estimates from my area will be different from yours. At the time of the estimate you will be told weather or not the water heater will need new B vent. I cannot see your entire install from here so it is impossible for me to be able to tell all the differences you may have on your job.