PS . If you now ride without bridel you can slowly but surely leaf your saddle in the barn as well. But you should be able to ride without saddle anyway. When your horse reacts responses good to your aids you'll be able to also ride without the rope.
Hope this helps.
You start by using the smallest aids while riding with tack. Concentrated on your weight and leg aids ( because you don't need the rein then). When your horse reacts good, use an soft leadrope around its neck for safety and soft direction. try not to use the rein. When your comfortable with that let the bridel in your tack locker.