Write a letter. Make it professional and thank her for all the experience you have gained but you need to move on.
This is a constant question a lot of people struggle with! If you want to be nice to your coach be honest with her. It’s hard cause they obviously have done a lot for you, but trainers also have to know that there are limits to what they can teach an individual. If they truly want the best for you they’d support your growth and advancement in the sport. It’s hard to bring up and it’s hard to talk about but being honest is the best way. There’s no real easy way around it!
Be honest! It’s good for her to know why you are leaving so she doesn’t make the same mistake again with someone else. Tell her that this barn isn’t giving you what you need at the moment and, although you liked it here, you think it’s time to go somewhere else and “explore” different things. Good luck!