I carry a 3oz bottle of dish soap which I just keep in my suitcase. I wash my glasses first thing and the glass or mug that I continue to want to use, I will put in a drawer so the maids don't see it. Then I just keep using the same glass/mug that I know I have washed and is clean.......
(I also carry a 3 oz bottle of vinegar, I will use that to flush through the coffee maker in the room. I get clean water coming out of there and so do the next set of people that stay in the room
)