As someone with anxiety it is safe to say that trusting someone, much less your significant other, is not the easiest of tasks. Regardless of how much I want to trust someone it is still difficult. Someone with anxiety needs reassurance, on the regular, that you still like them. They will constantly apologize for situations that were not their fault; do not let them blame themselves.
When dating a girl with anxiety, she will support you and be there for you, but will have trouble expressing or communicating to you how much you actually mean to her. Just remember she appreciates you, and she is trying.
Often times, dating a girl with anxiety also comes with a generous helping of the depression that usually tags along. Keep this in mind. If you are out somewhere with her and she stops talking, just know she does want to be there. She will need days away from you, although she may have a fear of being alone at times. She will also need days with you.
There will be nights where she does not sleep; there will be days where that is all she does. Some days she will do absolutely nothing, and others she will try to accomplish the impossible. Despite what she ends up doing for the day, she will never feel as though she has conquered enough. These maybe things she has not told you or you have yet to figured out, but that's why I'm here to tell you.
She tries relentlessly to trust you, although her dating history has been a toxic mess. She tends to keep to herself, but she also needs people to understand her.
Occasionally she will have good days. Occasionally she will have days where she has horrible anxiety attacks. Please be there for her during both. She does want you there, despite what it may seem. She cares about you, she just is not the best at expressing it.
Tell her how you feel about the relationship. Tell her how you feel about her. If you think she is beautiful, tell her. If you want to spend time with her, please tell her. Make the changes so that you are comfortable, but so her feelings are also validated. She will overthink and assume the worst; let her know that everything's going to be ok.
She cares and appreciates you. She will always have your back and support you whenever necessary. Remember this during her worst days.