If you are using Prime there is no need to let the new water sit for a long time. Heck, people who do water changes with Python-type water change systems add the Prime to the tank while the water is going directly into the tank...no buckets at all.
Leaving a bucket of water overnight is very old-school. It does no harm, but is not needed with a good water conditioner, like Prime. In my house, leaving a bucket overnight would guarentee a cat or two would be drinking out of it, and or playing with in it. Not ideal for fish health.