How do you show your girlfriend you trust her?
Well, coming from a girl who has had a Complicated relationship.
All you really need to do is be open with her. Tell her that she
can trust you, and be open about yourself.
And ask yourself, if you can't trust her than there is no way
she is going to trust you.
So just be open, be willingly to trust her and make sure she
knows your there for her and over time she will open up.