It is quite possible that the well got a shot of bleach because it either hadn't been used in forever or because it was known to have become contaminated bacterially for some reason. I'd not be nearly as worried about acute toxicity of the chlorine as I would be about the reason it got the bleach in the first place.
And for what it is worth, chlorine toxicity I'd expect to afflict you and your dog very quickly and pass quickly too, assuming it wasn't enough to kill you outright.
Thanks for the reminder to be a bit suspicious of water wells you stumble across out in the woods. Even though this was a park water supply, clearly it is not enough to just look and see, yup, it's water.