You’ll want to use your current pond water because that is what your fish are used to. It’s also already a stable environment for them. Tap and other water has chlorine and other chemicals in it your fish won’t take to well.
When you move your fish make sure to have a net over the tub so they can’t jump out. The tub should be in a shadier spot. They also shouldn’t be left there for more than 5 hours or so.
Draining your pond for cleaning can be done with a sump pump or clean-out pump. It may be best to rent one of these because they tend to be on the pricier side.