Is there an "adapter" that will allow me to connect the hose (i.e.
water in pipe) of an appliance (temporarily) to a bathroom sink tap?

In a word, yes, there is. In fact, you might get away with hose tap
adaptors. You can usually find one with the same external thread that
washing machine hoses like. Then you can just unscrew the hose when not in
use to get your tap back.

Christian.