We can't even reliably trust people to put the plastic bags in a bin and have that bin be cleanly collected and yet you're expecting people to bury them??
No, the solution is to massively reduce how often we use single-use plastic bags. It seems like every time I buy anything from any store its just assumed I want it in a plastic bag. Getting a single bottled drink at a convenience store? The clerk gets a plastic bag ready. Its insane.