Using a tarp and a blanket insted of a proper cover, is like using shower curtin for a bed sheet.

Most good bike covers will come with a sac to jam the cover in to when not in use. The cover will not only work a lot better(it will be form fitting with and elastic band around the bottom), but it will take up a lot less room than a tarp and a blanket will. Trust me you will never regret buying the cover.
Save your tarp for your wood pile.