First, there's no such thing as a "Garden" Snake. It's a GARTER Snake, and those eat small fish, small frogs, tadpoles, and earthworms. Second, we do not have Grass Snakes in the United States. That species if found in Europe, and it eats the same thing that Garter Snakes eat. We DO have Green Snakes, which are small, slender, bright green snakes that usually are found in trees. These are insectivorous snakes and eat primarily soft-bodied insects, but they are especially fond of non-fuzzy types of caterpillars, though some will eat crickets, as well.
If it is a rough green snake, it can eat small mice, flies, ants, and even frogs.
Green Snakes should be fed crickets and insects. Did you ask the pet-store where you purchased the snake, what to feed it. They usually recommend and provide you with caring instructions, etc. I would call them and see what they advise you to do. Good-Luck.
The rough green snake eats PEOPLE