"Chief Cook and Bottle Washer" meaning and etymology
Solution 1:
The main sense of the phrase I'm familiar with is: someone who is in charge of most all matters in an organization, both the important and menial.
I found a reference to the phrase in Early American Proverbs and Proverbial Phrases by Bartlett Jere Whiting which lists two citations:
1809 Linsley Love 40: I acts cook, steward, cabin boy, sailor, mate, and bottle washer.
1844 Hone Diary 2.705: Gen. Jackson’s chief cook and bottle washer, Col. Polk.
I also found an interesting reference from 1835 which referred to the Devil as being the "chief cook and bottle-washer of the slave-trade."
The earliest citation refers to "cook" and "bottle washer" as being just two of the many tasks the narrator needs to perform on board a ship.
Since the earliest citation refers to life at sea, I have a strong suspicion that the phrase originated in the sailing/naval sense. I haven't done any research in 18-19th century naval life, but I imagine that "bottle washing" was a task often performed on sailing vessels. I have to presume that bottles of rum, messages in a bottle, ships in a bottle — all these bottle-related naval tropes have some basis in history. Certainly a bottle-shaped receptacle for drinking is more practical on rough seas than water/grog/rum sloshing over the rim of a mug or cup.
Solution 2:
The way my Dad, a Navy vet, used to say it, it was "Chief, Cook, & Bottlewasher" (3 professions, not 2) and the meaning was that not only were you in charge, but you had to do all the middle management and menial responsibilities too...you did it all. Its not so much a derogatory term but it usually implies that everything is your responsibility, but you don't get paid/credit for all the job titles you perform.
Solution 3:
I can't share much of my own experience, but Wiktionary notes it as holding all of of the jobs, which fits with how I've usually heard "and bottle washer" appended to a list of duties, implying that the company is small enough, or cheap enough, that no matter how high your position, you also do the menial tasks.