Hi, I wouldn't reccomend putting plastic in the cage as bunny will shred this and it could be harmfull....instead lay down a whole newspaper under whatever bedding you are using...sawdust/shavings or hay/straw, this will soak up any wee and as long as your bunny is not too messy you will be able to pull out the newspaper with any mess intact on top of it! Believe me it makes it so much easier. If you already have the tarpaulin make use of it by fixing it over the cage as extra insulation or water proofing.... I used to tack it to the very bottom of the back of the cage then flip it right over to the front of the cage of a night....this stops the wind and rain from going through the wire mesh and keeps bunny snug....secure the front with bricks or if you're really handy attatch a lenght of wood to it to hold it down.
Hope this helps
Lisa x