You're quite right that a bath is a bad idea. It's not just the getting wet, it's the stress as well and a bath is totally unnecessary with a healthy rabbit. Only if a rabbit is very very unwell should any attempt be made to clean it, and even then it's not usually a bath like you'd give a dog.
If it's raining a lot your rabbit will probably choose to go inside but rain is generally fine as their coats don't get soaked. It's generally only the top part that gets wet and the underneath stays dry. If you want you can weatherproof the run though by putting something on top.
One last point, as you keep referring to one rabbit, rabbits generally do best in pairs so you might want to consider getting a neutered partner for her from a rescue. Having companionship is really important for rabbits, especially if they live outside :wave: