I feed my rabbits their hay by adding it to the top of their litter box twice per day. Yes, it will waste lots of hay. But they also pick through their hay even if it is fed some other way. They can be choosey about which strands they want. So even if you don't add it to their litter box, they will still waste hay (just maybe not quite so much!)
I'd suggest buying your hay by the bale or half bale. I cannot express how much money this will save you. A full bale of hay may cost roughly $17-$24 but it will easily last you an entire year! Feed stores typically carry bales of various types of hay.
I know from when I used to buy those bags of hay at the petstore, just how much that can be. But getting it by the bale is soooo cheap, that even if you threw half of it away, it is still cheaper, way cheaper, then buying bagged hay from the pet store. You won't need to fret over wasted hay and won't need to skimp on what they get.
It is a pretty natural habit for rabbits to graze while they potty. That is why having hay in the litter box is a good idea. By adding fresh hay on top of the litter twice per day, they will always have fresh hay to eat.