Hay is not bedding. It is most of the diet, and the teeth depend on it.
The pellet bag makes it look like pellets are the food and hay is a side dish. It's the other way around. Unlimited grass hay should be the large majority of what a rabbit eats, with a small measured amount of pellets and fresh greens on top. Timothy, orchard, meadow, brome, any grass hay is fine. Alfalfa is a legume rather than a grass and it runs too high in calcium and protein for an adult. It's right for babies under about six months and for a rabbit a vet has asked you to put weight on, otherwise treat it as a treat. Here's why this matters more than it sounds. Rabbit teeth never stop growing, and that includes the molars in the back, not just the obvious front ones. They stay the right length because of the long sideways grinding motion of chewing hay. Pellets get crushed with a short up and down chew and don't do the same work. Pull the hay and the molars develop sharp spurs that cut into the cheek and tongue, and now you're doing dental work under anesthesia on a repeating schedule for the rest of the rabbit's life. Signs you might already be there: dropping food out of the mouth, eating slower, going for only the soft stuff, damp fur under the chin from drooling, weight loss, and watery eyes, since the upper tooth roots can press on the tear duct. If your rabbit ignores hay it's usually one of a few fixable things. The hay is old and smells like nothing, so buy somewhere with real turnover and check that it smells green when you open it. Or there are just too many pellets on offer, so cut the pellets and hay gets a lot more interesting. Or it's sitting in a corner they never go to, so move it next to the litter box, because rabbits like to eat and go at the same time.