When the bathtub is running water out of the spout it leaks into the basement below. I have filled up the tub approximately 5 inches and let the water sit for an hour and there is no leak into the basement. I have also ran the shower for 30 minutes and there is no leak into the basement. The only time that it leaks is when someone is running a bath. The handle only has one knob. You turn it to the right for cold water and left for hot water. Any help would be appreciated.

Could be a problem with the pipe work itself and not the bath tub, try checking any connections too pipe work that is accessible

My guess is that your spout is the problem. Spouts slip on or are threaded on, guessing you have a slip on. Look for a set screw on the bottom side of the spout. Back o you for follow up