At the drink stations, I just fill directly to my water bottle - you don't need to purchase a mug. In the resort food courts, they also have ice machines. I typically fill my bottle up with ice and by the time I make it to the bus stop it's already started melting.
I used to only use a Brita water bottle, that way I could fill my bottle with fountain water and not have to worry too much about it. Well, I've had 3 or 4 Brita bottles have issues with the lid and I got sick of spending so much money on a water bottle. So my last trip, I decided I was going to just try to get cups of ice water when I got thirsty. I didn't last a day before I had to buy a reusable bottle (I'm glad I did, because it's super cute). I always asked for cups of ice water at QS locations and poured the cups into my bottle.
I will mention, I cannot drink the water out of the fountains unless I'm incredibly thirsty and can't make it to a QS location - it is nasty and not usually cold. But the cups of ice water at restaurants and the water out of pop machines is totally fine.