I used to use bagged ice. When I was doing partial boils I would put 16 pounds (two gallons) of commercial ice right in my fermenter. Actually, the IPA that mademy dropdown used that system.
What I would do was pour out ofmy kettle into a waiting gallon of cold water in my bottling bucket, whirlpool that and then out the spigot onto teh ice in the fermenter.
I never got burnt, but it is a variable, and it could hurt a lot.
Be real careful to check your bags for tears, and for goodness sake use the self checkout so a careless clerk doesn't tear the bag open on some germ laden grocery store checkout lane thing.
I built a chiller for about $50, so now I put the chiller in the kettle with the store bought ice in the kitchen sink. I use a pond pump (seasonal department, Lowes/ Home Depot) to recuirculate the ice cold water in the sinkthrough the coil. Pump was ~$25, 20 feet of soft copper was ~$25.
Fifty bucks is fifty bucks, but it takes a variable out of my system.
Pics link:
https://www.homebrewtalk.com/1391859-post33.html
Maiden voyage of my cooler will be either Monday or Tuesday, I worked this weekend; going after Mosher's Black Ship Pirate Stout as soon as I can get my work area clean.