Farm hay is not always better and rabbits don’t always like it more. Mites can lurk in all hay. Hay is actually a rather complicated subject. Good hay should be green and smell good and not crumble and – obviously – not be wet. But some things you cant see or smell, for example aspergillus mold spores. In principle, you can buy farm hay from conscientious growers. Harvesting and drying and storage must be properly performed. Hay for race horses must be of the utmost quality, or the horses can’t race. Cow’s hay is practically always too rich (cows need extra protein to produce calves and milk).
It doesn’t necessarily have to be timothy hay, orchard, oat or mixes commonly sold as meadow hay will do excellently. Alfalafa isn’t good for adult bunnies though, otherwise they can eat all types of hay that horses can eat. Horses and rabbits are very much alike when it comes to nutritional needs and the way they digest their food.
You could ask around for good hay suitable for rabbits, for example in local Facebook rabbit groups. A hay bale is pretty big, so if you only have one or two buns, you could perhaps buy a bale together with other bun owners and split it between you. Some farmers sell mini-bales or flakes of bales for small pets.