Hi Tyler
I can understand your pain. I broke up with my ex girlfriend one month ago.
Do not blame yourself for what you have done, but instead, reflect on them and try to change yourself, even a little at a time, for your own sake and for your girlfriend.
I think you can write her an email or hand-written letter to tell her that you are sorry and how much she meant to you and that she is special. Be kind and gentle in the letter(or email), do not give her any pressure, no guilt. Be honest with your feeling but write in a way that does not give pressure or blame.
Be honest but do not make yourself sounds desperate, now (in this letter at least) is not the time to tell her that you miss her so much you want to make love or you want to hug her(just an example here). But you can tell her you miss her because she is special in your life.
Show your gratitude to her in the letter, thank her for even the smallest things, example: the breakfast she cooked, how she helped to choose your clothes when you guys go for shopping. Again, be kind & positive in the letter, nothing heavy that will make her feel uncomfortable or confused
Tell her that you will always be there for her and she can contact you anytime when she need to.
After the letter, give her some space to think and recover, it is ok (and sometimes necessary) to have no contact for a few days or even weeks. And if you you do contact her or see her, send short “How are you?” “Everything OK?” “All the best in your work” type of emails to show that you care. If you do see/meet her, give her a warm smile, and a gentle greeting. Again, nothing heavy that will make her uncomfortable

I believe she have feelings for you, you just need to be kind and gentle to her, and give her time. I believe time and sincerity and your love.

This is just my own opinion.

Now that you are alone, use this time to polish and improve yourself (and change)
I hope and pray that everything will turn out for both of you

Lets us know how it goes. All the best

Howard