It's great that you are working with a trainer
and also that your girl is a well broke horse
I have a huge fear of heights. Going on a ladder(even a small one) scares me! So I completely understand your fear about being up on top of a horse.
Do you think you'd feel more comfortable if there was someone leading the horse and then people by your legs (holding onto your leg if you want). I used to do that when I worked at a horse camp. There were some kids that were terrified of being up there, but the fact that they knew that there was someone controlling the horse and 2 people holding onto them made them more comfortable. And after a while, they stopped holding onto their legs and just walked by them and then eventually they left and there was just someone leading the horse.
If that's not possible, maybe sing a song, or have one of your favorite songs playing on a radio to help you relax. Think of something that could help take your mind off of being up there :)
I also agree that you should spend a lot of time just bonding with your horse. Take her for walks (like you would walk a dog), hand graze her, give her a "spa" day, or a makeover :) There are so many ways you can be with your horse, without having to be on them :)