Guess what, you aren't the first to think about it.

bed sheet tarp

Here is a waxed canvas pack. You can read about how he waterproofed it.
Waxed canvas pack

Here is a tutorial on waxed canvas
Waxed canvas

Here is a guy that made a tarp from a bed sheet.
bed sheet tarp
He did it the way that I recommend if you want to use a bed sheet. Waterproof it with silicone.

I would rather make a tarp from nylon, much lighter, but, hey, try it out if you want.
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