When I did have rabbits, I used hay for bedding and it never proved a problem. It's more expensive than buying mulch hay or using straw or shavings, but in our harsh winters the hay was more insulating than shavings (not to mention we had the hay from our other animlas). I would stuff their "bedrooms" full of hay and they would much away at a hole and pat the hay down as they saw fit.
As I said, it might be more expensive, but you really won't use a lot of it, so you should be just fine.