How to control 1 PWM in MOSFET H-Bridge driver with current sensing IC?
The BTS50055 is not good for fast PWM. If you look at the data sheet in particular "load switching capabilities and characteristics" on page 3 it tells you how fast the device can switch. Turn on time is somewhere in the 100us range typically and turn off might be about 60us. These numbers need to be 1% or less for decent efficiency and 100us represents 1% of 100Hz. If your switching speed is pretty low then use it.


  How can I design a MOSFET H-bridge motor driver controlling only 1 PWM
  for a motor?


If I understand correctly you have a single PWM signal and you want to drive a H bridge with this signal. I'd start by looking for a couple of beafy N channel mosfets like the IRF1010 and then pick a topside/lowside mosfet driver like LTC4444. Feed PWM to the inputs via a couple of logic gates that create a deadband (so both FETs never switch on at once) and this gives you a half H bridge.

Repeat to make the other half but remember to invert the PWM signal. I'd look to be monitoring current on the dc side of things and forget about the BTS50055.