I don't waste time dripping!
It's not a good idea. It unecessarily stresses the fish which ought to get out of the tiny cage and into a nicer environment ASAP.
Here's what I do instead:
Float the bag only if it needs to be
cooled down to within a few degrees of tank temperature. If the tank water temp is warmer or within a few degrees, I do the following without floating the bag. Carefully pull the open bag out of a small clean bucket leaving the fish to swim a moment. Then, one hand holds the bucket on the lip of the tank, while the other
clean hand carefully lifts the fish (even Tangs) out of the water and into the tank letting it swim away on it's own. (Be careful with nervous, floppy fish like wrasses and damsels.)
You'd be surprised how much the fish appreciate this careful handling, rather than netting and/or spending forever in a tiny plastic cage, and it's nice to have that tactile contact with the new pet!