I have a favorite purple thermal mug from Death Valley that I just love because I doesn't have a handle on it (would not fit in my cup holder with a handle on it).
Any way, I always wash this puppy out at home really well with hot water and Dawn after Starbucks use and can tell you that I've brought it back for my latte on a number of occasions, had the barrista look inside my mug, then walk over to the sink and wash it out, because apparently my soap and hot water washout wasn't good enough.
So, I don't know what's doing on at other Starbucks, but my Starbucks in San Francisco, San Diego and Portland have been doing a great job of keeping an eye out for my personal mug.
I believe the issue here, as the OP perceives it, might be the bucket. Being the food industry, I feel certain that Starbucks has done samplings which have been plated for bacterial and mold growth, otherwise, I'd be getting sick, because my gut over-reacts to just about anything. What we also don't know is the temperature of the water and how often the water is changed out. Those two variables are important pieces of knowledge to have on board.
Perhaps the best thing for you to do is to express your concern to corporate Starbucks. I had a really bizarre thing happen once as I was standing in line - a line that was going no where. Stood and stood and stood and stood. My Dad was ill in a nearby hospital and I needed to get back to him with new pajamas and had stopped just to get an iced latte, but this was ridiculous. And, I was standing because there was no one to be found. Hel-ooooo, says I. Absolutely no one came out from the back. Then people started forming a big line behind me. Yo ho! I saw staff inch their way out from the back - but stopped and chatted and chatted and chatted. This as ridiculous! If it wasn't so hot outside, I would have been gone. At this point, I turned to the two gentlemen behind me, raised my right hand and made it do it yack-yack movement and pointed toward the entry to the back of house, because they couldn't see what was going on and I could, then just raised my shoulders like I really don't know what's going on here. I let another minute go by and again verbalize, Hel-loooo, followed by "can we have some help out here, please. You've got quite a line of customers waiting." Well that got them moving. After I received my drink and had walked about 30 feet away, the two gentlemen who had been standing behind me in line walked up to me and tapped me on the shoulder. The senior man introduced himself as Starbuck's Regional Director for western states!!!!!! And he had with him his Asst Director and the manager of the Starbucks I had just walked out of. He mentioned the manager by name and said that ______ had something to tell me. The manager was made to apologize to me and give me a loaded Starbucks card. The Director gave me his business card should I have further questions, etc.
I found this encounter positive in the extreme and praise Starbucks for the manner in which the Western Regional Director handled the situation.
(The Director and his Assistant were in that Starbucks to "shop" the store: e.g. check up on service, product, cleanliness, etc.)