I agree with Bunny House. Horse hay is fine as long as there’s no or only very little alfalfa in it. Horse grass hay is fine. Pooped on hay is not good though. If you have access to the bales when you open them, maybe you could fill a tote bag etc and take home with you? I’m assuming you have the giant bales, I’m not quite sure how tey work though. I have given my buns excellent quality horse hay, horses and rabbits are very much alike when it comes to digestion. Horses are often working though, so alfalfa is often mixed in with the grass hay, at least in the USA. Our house rabbits tend to do the bare minimum of work though, so alfalfa shouldn’t be given to them unless they are young growing rabbits, pregnant or lactating does or sometimes sick, recovering rabbits that need extra protein and calcium.
Hay silage has risks though, and I’d stay away from that. Horses are often vaccinated against botulism but rabbits are not.