If she doesn't like metal bits...you have two options. First trying with sweet iron bits, I had a great experience with them, specially the ones from TRUST.
Another option is to put her a Nathe bit, some horses just don't like the iron and the "happy mouth" ones are really an option to take into account.
However, all these problems should be observed when riding. These kind of horses just don't accept the iron and they tend to open the mouth and move the head a lot. Maybe it is just a matter of educating her...at the end she is only 4 yo, be patient :)
Also her teeth are fine, she's only 4 and has had everything checked out. I won't be starting her out bitless as she's pretty strong as it is. She's a cheeky little pony but there's no badness in her just a dislike of a metal bit. It's also just a snaffle not anything harsh.
Yeah she's a saint when you get it in. No problem lunging or driving. She's only getting tied up now for about 2 weeks but each time putting a bit in is harder and harder. It's not fear of the bit it's pure cheeky pony.
I use to give my youngsters oats with the bit on. Then they learn faster to place it in their mouth and they kind of forgets that it's uncomfortable.
Have you checked her teeth? Horses who has problems with their teeth is often hard to bit.
Then just take the time! Work from the ground and make the horse relax in the jaw. Massage the bit in the mouth until the horse learn to relax in the jaw. Then you can start to back the horse while massaging the bit in the horse's mouth, until the horse relaxes in the neck. Then you can go forward as a reward.