What kind of bit are you using and are you sure the bridle is adjusted correctly? My two-year-old was started under saddle about a month ago and because he has such a soft mouth, we actually downgraded him from a regular single joint copper snaffle to a nice fat french link snaffle that he loves. I know my BO and the trainer at our barn, who are working together to train Aires, both prefer to start horses off in the softest bit they'll respond to. Basically that means start in a snaffle, not a curb or something more harsh like that.
Also, how are you bridling her? Are you pushing the bit against her teeth to get her to accept it? If so, that will cause her pain and she won't like being bridled. If you put your fingers on the bars of her mouth (where the bit sits in her mouth) and apply gentle pressure, she should open her mouth fairly easily and you can slip the bit in with no problems. Just be sure you aren't banging her teeth when you put the bit in.
Another question...when were her teeth last floated? It may be a problem with her teeth that is causing her pain and causing her to not like taking the bit.
When you say you "show her that you're the boss" when she's being difficult to bridle, what do you mean, exactly? In my experience, the only time a horse resists being bridled as much as yours is, is when they're in pain or when they don't like the bit/bridle/something you're doing. My old gelding used to be ridden in a REALLY harsh bit (twisted wire snaffle), so he'd throw his head up when I went to bridle him. Once he realized that I was riding him in a nice, soft french link snaffle, he actually started dropping his head down and reaching for the bit himself.
As for getting her to move out from a walk...it almost sounds like she's getting mixed signals from you. How short are your reins when you ask for the trot? Do you have them pulled up tight? If your reins are too short, you're putting pressure on the bit, which is telling her to stop, but then you're kicking her to go, so she's getting confused (and likely frustrated).