Am i going about this right?

so getting to know my new horses issues, who is an ex race horse and had 18months hacking and a small amount of schooling and jumping since racing, and what i have to work with. shes not particularly naughty, jumps up to 2ft6 atm in trot and canter and comes back to me when i ask her and is good in open spaces and doesnt get strong or silly. our only real problem is that she is a bugger to get on the bit in trot and canter. she can do it perfectly, the first time i rode her she did a lap of trot in the school that was absolutely beautiful and she is perfect in walk and will do it in trot but takes a lot of work and fighting her. she is just really awkward if she doesnt want to and it is just complete ignorance. she has nothing wrong with her, we had her vetted before we bought her and shes all fine and her teeth were done 6 months ago. she has a definate stronger side and you can see that shes been doing this for a while because of her muscles in her neck and back legs but what she does is she puts her head up very high and puts her head to the left and clenches her jaw and pushes her body out to the right and its a pain in the bum especially if we are in the indoor school because those walls are very hard if she squishes your leg. and if you ask her once she will continue to do this every time you trot/canter because she thinks your going to ask her to come on the bit. so i have stopped asking for her to come on the bit for the time being except for lunging her in side reins twice a week. instead i am just focussing on her moving straight and evening her muscles out. so when she puts her head to the side i will circle her to the other way and do 10 metre circles until she bends properly and listens to my leg then when shes listening to me i will let her go straight and if she starts turning her head again i will circle her again. today i got her to stay straight most of the time even when i was trotting across the diagonal to change the rein and doing serpentines. i will buy her a market harborough soon as i used one on two other horses and they are brilliant and because any movement through the reins brings their head downwards it will help her loads i think and the groom from my yard (who is a very good rider and is very experienced with tbs) agreed. and if you use them enough to get the effect but then also ride without them sometimes and then use it less and less you dont need it at all eventually. currently shes ridden in a hunting breastplate to keep her head down a bit and stop the saddle sliding back, this is what she was ridden in before coming to us. her past owners have been much to soft on her and have let her get her own way all the time so thats why she is how she is.