It sounds to me the faucet to the tub is in need of repair. The diverter on the tub spout doesn't shut off the water,it justs diverts the water to the showerhead. If you know the mfg and model of the tub faucet, you may be able to get a rebuild kit at lowes or HD. More likely you will have to run to a plumbing store for parts, that is if you know who made it.

You probably just need a new washer in the tub faucet (providing this is the type set-up that has separate cold and hot faucets).
First, determine if the offending faucet is the cold or the hot. With the water for the house off, remove the valve handle, a screwdriver will probably be needed for this. Remove the escushion and then the valve stem (with a crescent wrench) and replace the washer on the end of the stem.
If it were to be a long term fix, you should also replace the valve seat.

rjoh878646 & randy427 - Thanks for taking the time to help out.

Its a single handle Price Pfister by the way - hopefully its just a washer repair kit rather than a cartridge used by Moen, as another poster pointed out on the Plumbing forum. What do ya think?

Thanks again.

Found a PDF for parts explosion on their website

Here is a link that might be useful: parts explosion

rjoh878646 - Thanks for the PP schematic- I called PP and the valve/cartridge is on backorder - will send asap they said. I put my old one back in in the meantime. Thanks again.