I was going to suggest things like:
Dried legumes (beans, split peas, lentils, etc - in bulk if possible), Cabbage, carrots, whole grains (various types of rice, oatmeal, etc - in bulk if possible) and what not. Honestly, $135 should be plenty for 1 person. I don't really have a budget but my husband and I spend between $250-$350/month on food for both of us. And honestly, a lot of our food is organic but because we don't eat meat, our costs are fairly low.
I would check your local library for some cookbooks to help you with some recipes: vegan on the cheap, supermarket vegan and more-with-less are 3 books I can think of that would help.
This is a blog of a woman that used to spend $100/month for her and her son. She has quite a few tips/tricks for eating inexpensively: