In the end, my best suggestion would be for you to base your circuit on some form of Step/Direction stepper driver. Feed your frequency into the Step and pull the Direction either HIGH or LOW as you wish for stepper direction.
Just be sure to pay attention to what the max frequency the circuit can work with. If you try to send a 20kHz pulse into the Step pin and your circuit/chip can only handle 5kHz, you will at best get a skittish stepper, and, at worst get an immobile stepper.