Cruelty to Bikes is one thing but If you have to- then get a Goretex cover to put over it. Feel certain you can get one custom made somewhere for around $1,000.

Problem with a Taup will be condensation- Problem with a sheet will be a wet covering permanently round the bike. Spray the bike with a light oil if you can and in particular on anything steel. Then use a taup but loosely covered to allow moisture out. And on bright sunny days- Take the taup off and polish off the rust before re oiling.