Hi Alex
Folowing on from what DB and others have already said, I've coined a phrase for the time spent at the sink chatting to madam, I call it "Kitchen sink marketing". This is a facet of our industry that many cannot grasp, ie one of the most important things you can give to your customer is Your Time
As for the protocol, I will always ask if madam has a utility room with a sink, and if not if it's ok to use the kitchen. I would only reluctantly use a bathroom tap as I leave my machine downstairs. I do occasionally take (hot) water with me if there is a known supply problem on site. I'll take it in 20 or 25 litre containers. A larger volume of water stays warm longer. If you wrap the container in an old jacket or similar, it will retain it's heat for several hours. Decant into a bucket as the container may "glug" causing considerable spillage. ALWAYS dispose of waste and surplus fresh solutions water down a toilet (prefered) or foul drain. NEVER into a storm drain, whether in the street or around the house. The fines are considerable.
It's always very nice to show a customer the dirty water from your machine, but when you've clocked up a few more years in the industry, you seem to take it for granted. But be careful. Madam may have had the carpets cleaned before and the recovered solution may have looked like Guiness. You may come along and by doing proper and thorough pre-vacuumiing, there may not be as much visible soil in the water so it may cause concern if she initially thinks you haven't done as "good" a job as the previous tech.