Want cheap and breathable? Try house wrap like Typar, Tyvec, or similar. Sew, staple or use a strong tape to join seams. If you make a tube, the bike could be wheeled inside and the openings rolled closed and secured with clothes pegs borrowed from the laundry line. If you then cover it with a tarp that is staked out like a tent to keep the worst of the wind/rain/snow/sun off of it, it should last a number of years.
Most home owners who have done any renovations will have left over wrap, so cost should be minimal. If you find 2 or 3 shipping pallets, you will have a nice platform to put the bike on, with air flow underneath to prevent ground water from wicking up.