If it is coming from the tub spout then the gasket is moving around or esle it is shot. The easiest way to fix this is to get a new tub spout. It will more than likely take more time to attempt to change the gasket on the spout then to install a new one.
It doesn't but you better run sir/madam their may be a ghost in your bathroom.
turn on the heat
There may be debris or sediment blocking the water flow specifically to the bathtub and shower faucets, which is not affecting the toilet and sink faucets. This could be due to a clog in the pipes leading to the bathtub and shower, or an issue with the faucet itself. It is recommended to check and clean the aerators or call a plumber to investigate further.
More "VOLUME" flowing from the tub spout then the shower head as the shower head has a flow restrictor
Often a faucet will sputter if there is air in the lines. This happens if the water has been turned off and then on again. If this is the cause, it is only necessary to run the water a while and the air will get out of the lines, and the sputtering will stop.
They both run
One of the things you do after a run is a post run warm down. Other things include drinking water, having a snack, and showering are also things done after a run.
The tub spout diverter,is just worn out.Go to your plumbing or hardware store and buy another with the same installation properties.(You may want to remove the old one to see how it was installed)
Defective divertor
I just installed an American Standard kitchen faucet and it continues to run for a second or two after turning the handle. I called AS and they said it is because of the high arch and the location of the stop valve lower in the fixture. I think it may have more to do with this being a lower end kitchen faucet. During a bathroom remodel we installed a high arch Pegasus bathroom faucet and, while it is admittedly not at high as the kitchen faucet, it stop immediately and doesn't continue to run/drop at all. When I removed the Pegasus faucet filter at the spout, it behaves just like the kitchen faucet, so there's some sort of stop valve element at the spout of the Pegasus that isn't part of the AS faucet.
To install a water filter on your faucet, first, unscrew the aerator from the faucet. Then, attach the filter to the faucet and tighten it securely. Finally, run water through the filter for a few minutes to flush out any initial debris.
Very simple. Run each faucet until there is no more air. This usually only takes a minute or two per faucet. Remember air is lighter than water and will quickly rise, thus exiting the faucet additionally the strong flow of water out of the faucet is a huge plus.