I wouldn't use plastic bags, as this is still going to be almost 200 F wort at the start, so the plastic bags aren't quite hearty enough and may melt.
Plenty of people on this board sanatize plastic bottles, fill them with boiled then frozen water, and submerge them. I'll tell you that it isn't going to speed up your cool down THAT much compared to an ice bath, and it can't be more sanitary than an ice bath, since you are actually putting plastic into your wort.
I transfer from my newer SS kettle into my old aluminum kettle before my ice bath. Aluminum conducts heat and cool much better than SS, which is a bit of a disadvantage in mashing/boiling, but a distinct advantage in cooling wort. I can go from 212 to 70 in my aluminum kettle in right at 18 minutes with 25 lbs of ice in my sink. I recently got a plate chiller for Xmas, so I'm all done with that here soon as well.
I'd stick with the ice bath if I were you and start saving up for a immercian chiller, counterflow chilller, or plate chiller, each of which can be had for around $60-90.