Have you tried riding in a simple halter? that's always my first attempt at bitless with a horse.
How is the horse in the round pen or on the longe? Is it reactive to your voice and body language?
My own way of handling non response in a horse is first seat aid, second leg supported with voice, then lastly a wake-up tap with the whip. If a horse isn't very educated to seat aids then I'd give seat and leg at the same time very quickly followed by the tap of the whip if I don't get a response.
What's in their mouth (or not) shouldn't make a difference in the horses reaction to your driving aids unless you're riding with the emergency brake on in which case a bitless bride won't make much of a difference.