There are a couple of ways I can think of to make the H-bridge much simpler to control. Essentially what we want is to add an over-all enable line to the H-bridge so we can use one enable line controlled by PWM rather than using a complex H-bridge driver. One way is to add another transistor to the circuit that only connects the bottom rail of the H-bridge to the negative supply. Pulsing this will make the motor run only while the control is high so PWM on this would make an overall speed control without having to worry about which direction the motor is running. The cost of the extra transistor could be quite high if you're using high power transistors or MOSFETS and depending on your voltage rails this might be eating into your motor voltage as there'll be a 0.7-0.4V drop across each transistor or MOSFET. The other option then is to use logic to filter the control lines so that the PWM signal is combined with the direction signals.