A specialized stepper driver such as the Easydriver has the ability to limit the current to protect the motor - there is a small adjustment potentiometer. Study the Sparkfun webpage.
With a h-bridge you will just have to limit the current by limiting the voltage.
Many h-bridge datasheets show how to connect them to a stepper motor even though they are not ideal for that role.
Now that I remember, you need 2 h-bridges for each stepper motor.
If you are just using low voltages the Pololu DRV8833 dual h-bridge may be suitable. However study the data on the Pololu website carefully.
...R