The horse will respond to the bridle differently (better) but will respond to your other aids quicker if you are using them correctly in the first place. Please read my previous posts on using the aids. The problem that most riders have is that they are under the illusion that they are in control of the horses they are handling. Anyone who has a burning need to be in complete control should take up riding motorcycles.

Building a trusting relationship with your horse is the first step, which you have already taken. Introduce new things slowly and in a relatively quiet, safe environment until you and the horse are completely comfortable and the new thing is "old hat." Most riders get into trouble by proceeding too fast for the horse's ability to cope. You know your horse best, so watch for signals that indicate insecurity, fear or discomfort. You need to have your horse balanced and confirmed in all the aids at walk, trot and canter in a fenced area before you take her out on the trail. Then take her out with old, wise trail buddies on quiet, not challenging trails, until she trusts your judgment in the new situation. If it takes a year of training in the arena before she is balanced, responsive and STRONG enough to go on the trail, you must be patient enough  to give her that time. 

A fatigued horse will rebel, so start with very short rides. Remember that horses fatigue emotionally and mentally as well as physically. Don't push her past her ability to cope.  A young, not fit horse has about 10- 15 minutes of good coping power. After that you must be very vigilant to watch for signs of fatigue.  Build up the time gradually. ( i spend 10-15 minutes doing a warm up of walking and trotting on a longe line, followed by 20 minutes of good dressage exercises and then a 15-20 cool down of walking either in the arena, or on the trail with a trained horse.) You should start out longeing a young horse until it is "legged up" enough to support your weight for an extended time comfortably. This way you will avoid having the horse learn to buck when it is uncomfortable.  You haven't said how much instruction YOU have had in the correct methods of starting a young horse so i don't know how detailed to be. If you have no training or experience, you need some good eyes on the ground to keep you safe and on the right track.

Always quit when things are going well during the first year of training. You will both  benefit greatly from this policy.