JPD350, I disagree with Eagle on this one. The purpose of using the meat immersion method is to rapidly cool the meat down. If the meat is already "as cool as you can get it" then you don't need to use the immersion method. Just my two cents.
Eagle, the condensation you refer to is accurate. But, condensation and blood drainage will cause your meat to get wet inside the plastic bag, regardless of whether it is cool or warm. The plastic bag just helps keep sediments, water contaminants, and fish or critters from eating the meat. In the larger picture, meat that been soaked inside a plastic bag with immersion therapy is doing better wet and cool than it would otherwise be warm and dry.
Once the meat is cooled properly inside the bag underwater, meat is removed and hanged or stacked onto shore debris to allow drainage to fall off the meat and the air to help dry the surface. After it dries, the meat can be replaced inside fresh game bags.
But, JPD's question was about boggy stagnant water source as he finds the bull, before and during butchering. The best way to go about this is to cut a bunch of willow or alder brush and pile it next to the carcass so that when weight is applied to the brush pile it doesn't sink, on the side you'll peel the hide toward (i.e., pile near the belly of you skin from the spine). The hide is peeled off the carcass and then laid down over the brush pile to provide a platform or makeshift tarp where meat is laid before it's bagged. You might consider making two piles, one on each side of the carcass and then split the hid about mid section of the belly, filleting it off the carcass with half going toward the belly pile and the other half laid on the spine pile. This should give you good protection from the water.
But, you'll undoubtedly get meat wet in the process at some point. The best thing you can do is rinse it off in a river or clean water source if the source water was stagnant. Then, spray the surface with a strong mixture of citric acid wash (2-oz powder to 1-qt water). This will retard bacterial growth while you transport the meat to your butcher. Reapply the citric acid wash every other day for best results.
Hope this helps,
larry