I just have to put in my two-cents worth...so take it for what it's worth
Nothing you have said sounds to me like your horse is doing anything dangerous, or that you can't handle it. In fact, I'm wondering if this horse is the one in your avatar.
If so, this horse will be a piece of cake to break. You just have a little bit of a spoiled brat syndrome going on. However, just like a kid, it can start out pretty innocent, but can get out of hand in a hurry if you don't correct it quickly.
You are going to have to train her with a saddle and a bridle. Just accept that. You are not going to train her, with any precision, bareback with a halter. There may be folks who can, but they get paid thousands of dollars to do that. You're not in that class...neither am I. Train her first, then ride her bareback all you want!
You have to be able to control her head with authority. That starts in a halter and lots of ground work. Then you bridle her with a bit (I like to start in a simple O-ring snaffle). Then you saddle her up and do more ground work (I actually like to saddle first, then bridle). Then, when all that is going well, you step into the saddle. That's where this horse will be a piece of cake, compared to others I have known. Now you start doing from the saddle what you trained her to do in the ground work. This process will take months, not days or weeks, to do it well.
I also recommend the use of spurs. When properly used, they seem to greatly enhance the horse's ability to learn and retain training, and seems to make them much more willing to comply with simple cues. Seldom do they need to be used roughly if they are introduced early in the training, before bad habits develop.
Now, after you have done all the above, and she decides to lay down and roll on you, a few good jabs in the ribs with the spurs will break that habit very quickly. When she tries to lower her head, you take her head to the side and don't let her get "the bit in her teeth", so to speak.
It all starts with ground training. That's where the beginners always skimp, because they are anxious to get on the animal's back and declare it "broke".
Remember, a lot of folks trying to help you here are basing their answers on their experience as show riders and trainers. You are not going to make a blue-ribbon show horse out of this one without help from a pro (or at least a very good) trainer, as has been suggested.
However, there is absolutely no reason why you
can't make her into a good, reliable pleasure riding horse.