Once your horse is settled (wise of you to give her time to do so), if you can ride her some on a really lose rein, you might have a chance to experiemtn with letting her go where she likes. It's called, "cruising". This helps build the rider's confidence in just going with the horse, and it builds the horse's responsibility for carrying the gait that he's asked to do.
You just ride in an enclosed area , such as an arena or large round pen if that is better. you set the horse into a gait (walk or trot, usually) and you hold the rein with zero contact. Horse can go whereever it wants, can put its' head whereever it wants can look anywhere. It MUST stay in the gait, though. So, your responsibility is to go with your horse, stay out of his way and mouth and only step in to correct him if he stops or changes gait. He must stay moving. This is a really good excersize to do . If she puts her head down and comes to a stop, you apply your leg, but do nothing to the rein.
REally challenges your trust. But only if you feel she will not buck or bolt.
The bit should be fine. It looks ok, though for some horses with a very low pallete, it might be a bit on the fat side.