I'd say go for it. Dollar store shower curtains are great too. The bubble wrap will likely trap heat from the sun and warm the soil faster. Here in my zone, raised beds warm faster than the soil around them. Especially during cool wet springs like the one we had this year.

Drill a few holes on the sides of the container as well. Holes on the bottom tend to clog and cause too much moisture to be retained.

I used a clear plastic tote from the dollar store about that size last year. Like the 7.00 or 9.00 size. I put plastic (came from a new quilt purchase) over it and cut small slits all over it. Drianage holes in bottom. Worked just fine.

You can also go to your fabric store,and buy some really nice clear plastic table cloth by the yard,that is what i do.Works great,there are a few different thicknesses to choose from,and not expencive at all.
cAROL

Thank you token, gardencrazy and cAROL. I love the dollar store. I bought clear plastic shower curtains 70" X 72" for $1.00 today. Using tokens suggestion, they had big heavy duty plastic bags like the ones token used from her quilt and also sweater storage bags (2 bags per pack for $1.00). I ended up buying the sweater bags since I figured if I didn't use them for WS I could actually use them for sweaters! token, I really like your idea because both kind of bags have zippers which I hope will make it easier to sort to peek in on occassion. The sweater bags are not huge (15" long, 12" wide and 3" deep) hmmm, come to think of it they are probably not deep enough to use - oh well, protection for a few sweaters. The light bulb went just went off why I should have bought the exact same one as token used - depth for the plant to grow. Back to the Dollar Tree! I haven't yet but will go by JoAnne Fabrics and check out plastic table cloth by the yard. That's another great idea.

Thanks again, I appreciate your help.

Zahzeen I took the plastic zippered bag that the quilt came in and cut it open and put it over the top of the storage tub and tied it on with some jute.
After you plant out the seedlings those clear plastic tote tubs also make great humidity chambers for rooting cuttings. Just put the lid back on it. I have rooted hundreds of cuttings in them.

Thanks, another option I came upon at Lowe's (they were selling their $2.68 small houseplants for $.10! - I got 12), was drop clothes. A 2ml thick drop cloth measuring 9'X 12' (108 X 144 inches) was $2.98. The only problem was that although if I held my hand close to it, I could see my hand, the plastic was just a little opaque. Since this is my first time wintersowing I thought I better stick with the completely, absolutely, unquestionably, most decidedly so, clear-clear plastic. They had the same size at different ml thickness. For $1.00 at Dollar Tree, the clear plastic shower curtains were a good deal - they are 70X72 inches. I did look at JoAnne Fabrics but the least expensive clear plastic was $2.99 a yard (would be 36 X 52 inches). There is probably less expensive plastic you could buy at a another fabric store, but for now Ill use the shower curtains and sweater bags. If I hear that very light opaque (almost but not quite clear) is OK to use, I might try the drop cloths suggested by one of the Lowe's employees. I picked up for $2.99 each at the thrift store a rubbermaid container (43 X 19 X 6.7 but no top) and a plastic toboggan for small children (48 X 14 X 4). The rubbermaid container is perfect (it even has wheels) but I think the toboggan may not be deep enough to sow seeds in directly. The toboggan will be useful for keeping together a bunch of styrofoam cups and be able to move them around if I have to. Now off to drill and fill them and the baby bath in preparation for the 21st! Thanks again for all you help and suggestions.

psstt milk jugs are opaque....
I think it helps keep the seedlings from cooking just a guess... everything I did with a clear cover in 08/09 had a lot of problems with poor germination...