Returning to a Taurus; Help Needed

First off, I'm an Aquarius male who dated a female Taurus two years ago, naturally throughout my life i had many trust issues with people and couldn't fully trust them. this is a big no-no and the reason why my girlfriend decided she didn't want to be together anymore. after going through crazy amount of withdrawal, I decided I still loved her, I tried everything to apologize even going as far as to write an apology letter to her. I gave the letter to my friend to show her, she got confused and left, the next day she returned to ask her if she could keep the letter. Now, we sit next to each other in chemistry class and she sometimes says things to herself seeming like she wants someone to start a conversation with her. i don't really understand Taurus women that much, but I understand enough to know that I still love her. What are the things that I can do to so I can be together that her again? I'm determined to push through anything as long as it will lead back to what we once had. Advice? Gift Ideas? Date Ideas? Just a plain follow this set of instructions and you'll be fine?

-Aquarius Male.