My bath tub crains slow what can I do?

OK you can try a few things. Plunging may be of moderate help if you cover the overflow plate with a tightly held damp towel. This opening is an over flow entry point but also a vent for the tub trap, it allows air to move back and forth and would negate plunging. If that does not work then remove the same overflow plate and use a 1/4" snake down the drain pipe. Before doing too much of this be sure to check the drain which frequently gets clogged with human hair. I use a Zip-It Unclog Drains in Seconds (http://www.zipitclean.com/) for about $2 at Home Depot. 90% of the tub drains I have seen are cleared by this method. If these three ideas do not clear your drain just let us know. I am assuming that you have no access to the trap below the tub, right?

I agree with Bob 100%, would like to add my two cents also that I have nothing to do here away from home.
You have a clog downstream from the tub that has to be snaked and cleared. This can be snaked from the tub waste and overflow, (see image). Unscrew and remove the overflow plate, (The one with the drain lever) and pull out the tub stopper if you have one. Now have a clear shot at the trap, feed the cable (1/4" best or 3/3" with a small tip. You can rent a Ridged K50 sink cable.) About 2' down you will run into the bend of the trap. Crank and push at the same time to work around it. Your blockage will be found in the lateral pipe going to the stack. You shouldn't have to put out more then 10 or 12 feet. The tub shower clogs to be mostly hair and the worm should auger into it and pull it back, good luck.

John