For my experience as a 27 year rural volunteer firefighter, it seems to me that getting a round bailer ready should include installing one good sized fire extinguisher on the bailer, a second on the tractor, and most importantly, assuring that you could uncouple the bailer from the tractor easily, should it catch fire.
I can recall most years, attending at least one bailer fire. Half of those events also took the tractor, as the operator could neither extinguish, nor uncouple. Upon noticing a bailer fire, uncouple first, get the tractor away, then consider fighting the bailer fire is safe. Sure, your cell phone works, and 911 works, and the fire department will arrive as quickly as they are able. Can they figure out your path to that field? Will their truck make it into the field?
We never saved a bailer. We lost a bunch of coupled tractors too. To add insult to injury, a burned tractor and bailer are both expensive, and useless for getting out of the field. At least if you can save the tractor, the fire fighters will help you couple the bailer back up after it cools, to get it out of the field.
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This was a friend's tractor and bailer, 15 minute drive from the fire station. Added concern for the hydro wires he just happened to burn under. We did get our second fire truck stuck in the lane to the field for an hour. It could not get more water to the first truck, and rendering it, and the truck at the scene unavailable to return to the fire station to be ready for any other fire call. Dave told me that he was not carrying a fire extinguisher at all that day....