Well to start with, this is difficult.
If it was me, I'd think about this problem and its solution in very very slow terms. I wouldn't plan on hunting with her this fall.
I would start with the shotgun out in the house for short periods of time (just a few minutes at first), with no one touching it. Like its a piece of furniture. Randomly drop some treats on the floor so she gets some positive reinforcement. Do this a few times a week. If she shows concern put it away for a week, and try again. Don't put it too closer to her bed, but against a wall in an open space, so she sees it and doesn't feel threatened. Slowly increase the amount of time but watch her carefully, you don't want her to show any fear. I wouldn't even pick the gun up around her though, until she is comfortable having it in her vicinity. When she is to the point of showing no fear with the gun in the room for a bit of time I'd transition to the field.
I'd have a friend carry the gun, behind me and the dog, say 50 yards (maybe more depending on how scared she is). Do this several times over the course of a week or two. Each time the gun is slightly closer to her. Let her run, have fun and ideally point a bird. The idea is the gun is just something you're carrying, don't show it to her or give it any attention. After success with this a few times I would wait until she is fully focused on running (ideally chasing a bird) and then have my friend rack the gun one time and one time only. Hopefully she shows no concern, but either way put the gun up and let her have some fun. I'd repeat this exercise over multiple days (again don't rush it), slowly having the gun closer to her until she is completely ignoring the gun. At this point I'd switch to a .22 blank gun and repeat the whole thing over again (ideally with birds). When I had my friend fire I would want him to be closer to 100 yards from the dog, while she is chasing or watching a flying bird. Only one shot. Repeat the same exercise over multiple days slowly getting closer to her. If she ever shows the slightest concern during any of this (watch for dropping tail and ears) take a week off and back up a couple steps. You want to be 100% sure she is not gunshy. That is a very difficult problem to correct (some would say impossible).
Good Luck!