I would think it is like putting fish in an aquarium. You get the new fish in a plastic bag pressurized with air. You don't dump the fish straight into the tank, but put the bag in the aquarium so the temperature in the tank and the temperature in the bag equilibrate and there is no shock from a temperature change when you dump them in the tank.
Just do the same thing. If you can't put the bucket in the water to let it adjust, slowly add the lake water in the bucket so the temperatures adjust. Thermal shock is all you are trying to prevent. Did your bucket get hot in the sun or is it still cold from the bait shop tank.
Hopefully I'll be to tossing my 12' cast net for bait this week. I've stepped up in size. It should be embarrassing for a little while

I actually haven't thrown a cast net in a couple years. It could be funny.