Bridling her inside is safer, because she won’t have anywhere to run off to, possibly dragging you. She is not a baby, although she is still young. That is just my opinion, after 57 years of experience (mostly with racehorses). My Arabian mare was much worse with the halter while in the field than ever with the halter or bridle while in a stall. My Arabian gelding and Morgan just always stuck their heads in whatever when I told them to put on their clothes (I am odd), and Selena is now doing as well as they do, at least for me. She is still difficult with other people. The Morgan, purchased from a kill pen in December (she only weighed 712 lbs) paced a LOT for a couple of months, but has now settled in and has two very nice friends in her field. Everything at your place is new to her, you are new to her, and she will probably settle down just fine – time is all important. Every time the two of you interact, you are both learning something. We all have stories of things our horses do that no one other than another horse person would ever believe (Selena is afraid of eggs and small children, and Joe Joe thinks there are dragons lurking in the bushes to steal his peppermints).
It is never the horse's fault