Can I use the the plastic wrap for this amount of time without damaging the furniture or will I need to preform additional preparations or seek another solution?
I don't think you can assume that type of plastic is safe for long-term direct contact with some finishes, varnishes in particular and some lacquers (it is very likely the bed is varnished or lacquered). There are many soft plastics which cannot safely be left in contact with modern finishes over the long term due to issues of migration of the plasticisers out of the plastic, which sort of melts the finish.
Unless you were certain of the plastic type and its safety in this regard I wouldn't want to risk it myself.
The good news is that under normal circumstances you don't have to wrap or even cover modern furniture that isn't in use, even over long timeframes. While draping in a sheet is traditional, and is still widely done by some, the reality is that it's far less necessary today with modern furniture because almost all has a hard coating. This is in contrast to much period furniture which had soft or relatively soft finishes which could easily be marred just from having dust sitting on the surface for extended periods. In addition, modern homes are inherently substantially cleaner than houses in the past, in large part because of the lack of open fireplaces. As you mention your basement is finished I would presume it's not substantially different to the rest of house in regards to dust.
So except for the issue of your cat I wouldn't worry about it and just trust to the finish to protect the wood. A quick wipe down, maybe with furniture polish, might be all that's needed to get the bed back to looking exactly as it does now in a few years when you put it back into service.
The desire to use plastic is because I have a P.I.T.A. cat that likes to mark her spots.
I'm sure you know this already but the best solution to that particular problem is not to allow the cat access to where the bed is. Easier said than done I know!