The earliest reference to the phrase that I've found in print so far is from 1835, in the New York Knickerbocker magazine:
'Pretty good reasoning, friend Seymour,' said I: 'you've made it very
plain, that the DEvil is chief cook and bottle-washer for the
slave-trade. I don't wonder it prospers so well, since he is at the
Another reference is found in 1843, and this also confirms the way my own father used the phrase, in that it refers to two professions, not three.
The sentence come from The Weekly Globe, as US publication, from the July 14th, 1843 edition:
We can assure the chief cook and bottle-washer of the hard-cider
campaign that he must make some other disposition of his dregs
The two profession option makes sense to me, in that one is at the same time at the top and bottom of the pecking order, with regard to a work situation. Hence, one is responsible for the entire operation from top to bottom, singlehandedly.
There is a singularly splendid passage in The Life of the Late General William Eaton, dated July 20th, 1799 that runs as follows:
I am sorry that the request of the "female Bocris"* is inadmissible,
being much disposed to serve them. But, I have already employed a
"hack sansal" from among the dispersed, who serves me as a drogoman,
broker, footpage, groom, scullian, bottle-washer, aid du corps and
physician : who was born in Gibraltar, is free of London, a convict
from Ireland, a burgomaster of Holland : was circumcised in Barbary;
was a spy for the Devil among the Apostles at the feast of Penticost,
and has the gift of tongues : has travelled in all Europe, and will
undoubtedly be hung in America, for I intend to take him there. He is
the most useful scoundrel in the world. He interprets, trades, runs,
holds a horse, scrubs, makes punch, intrigues, fights and prescribes
for me, for the moderate sum of five dollars per month, and the
perquisite of purloining every thing which I cannot miss. I regret
that I cannot oblige the ladies.
*Two ladies in Algiers, who wished Eaton to take one of their men servants.
This is the earliest reference I've found to a list of occupations, including bottle-washer, used to indicate that a person is a jack-of-all-trades, reminiscent of Jean Passepartout in "Around the World in Eighty Days".