Most of the time, problems are caused by humans, knowingly or not.
Horses need a reason to bite, and if they're not a testy sort trying to express dominance, they may be trying to communicate discomfort or stress.
With a horse that doesn't normally bite, I would check saddle fit and hooves before any "correcting", as well as watch for signs of ulcers which can be exacerbated by the stress of trailering and showing.
If pain or poor handling was ruled out, the next step is to establish personal space. Lots of equestrians, especially in the english discipline, make the mistake of letting the horse hang out on top of you.
I learned differently with the natural horsemanship clinicians... there should always be a respectful space, the only one allowed to close the gap is the human.
To enforce it, first make sure you have a responsive back-up. Then in every interaction use the back-up to set a boundary for the horse. Gently, patiently, consistently.
If they can bite you they are too close. If you're very consistent about it and instruct everyone who handles the horse to be consistent, she will respect it.
On a related note... some horses can develop peculiar issues. When I bought my horse Bear, he had metal rings installed in his gums. Bull Rings, they called them.
The stable I bought him explained they had rescued him from a terrible operation that left the horses stalled 24/7 when they weren't being ridden (infrequently). He was still a stallion at the time and extremely frustrated. So he would lunge at the walls with his teeth bared and bang his teeth against the surface. They said he was so loud with the banging, and scary with the lunging, that's how he got the name.
The first thing they did was have an equine dentist out, who found he was bending his front teeth back. So they hurried to get him gelded and gave him pasture time and exercise, but he kept it up. The dentist came up with the idea of the rings, and inserted each one in the gum between the teeth where there is a natural gap. 4 in total on the front upper ones. Every time he banged his teeth it hurt, so he stopped, and his teeth recovered. They told me I could either have them removed or wait for them to fall out naturally, which they did and never caused any problems.
And by the time I got him he was a total sweetie of a horse.
