Bareback is a wonderful way for riders to become more balanced and learn how to truly feel and move with the horse. But you need to remember, saddles muffle your cues - most people find horses are more responsive bareback. But if your horse is sensitive to being ridden in a saddle, bareback is even louder and more uncomfortable.
I'm going to put money down that she has pain somewhere - or that she doesn't know what the cue means. When I get on a new horse they always investigate my legs, when I apply pressure, they'll often look at my legs, nose at it, or fuss in some way or another trying to relieve pressure - it's not very often that moving forward is their first guess on how to relieve pressure.
So here are my thoughts - ground work! Do you do all sorts of yielding practices on the ground? Does she yield her hind end, front end, back up, will she side step?
If on the ground you put pressure on her side where your leg would fall - what does she do? Does she get upset then? If yes get a vet out - if no it's time to build her yielding and your dominance. If she yields perfectly on the ground, but is still upset being ridden I'd suggest her back or legs hurt in some way.
I think we really need more information. What sort of training has she got? How long has she been acting this way? Has anything in her diet changed? What skills can you do with her - ground and mounted? What is her diet now? When was her last teeth floating and vet check? Has she ever had a chiropractor or massage therapist?