Alive? Set down a humane trap. We had a mouse in our shed where we kept the guinea pigs in England, and my mum just went to a hardware store and bought this trap. It’s shaped a bit like this ‘_/’ and you set a bit of mars bar (Mice are quite partial to a mars bar, we found that out after several days of the trap being laid and nothing happening, then, mars bar, and BAM! Mouse caught! Hehehe!) and wait. It has a door on the other end of the flat bit, and you put your mars bar in the end of the diagonal bit. The moment he walks onto the diagonal bit to get the mars bar, it tips shut so the diagonal bit is flat, and the door shuts and stays closed via a magnet. My dad then took the mouse in the trap, drove about 45 minutes away and let it out in a field. Bye bye mousey.
Dead? Get rid of the hay, it’ll be contaminated and then switch to a different hay bale supplier.
P.S Sorry if my trap description was rubbish and confusing!