??? to the best of my knowledge it either comes from a former british prime minister Lord Robert Salisbury(Bob) putting his nephew into various government jobs (hence bobs your uncle) or from an old music hall song that has a line "bobs your uncle, follow your uncle bob." hope this is some help.
First, are we agreed on its meaning? How about:
"Bob's your uncle is an expression of unknown etymology, commonly used mainly in Britain and Commonwealth nations. Typically, someone says it to conclude a set of simple instructions to mean, "And there you have it", or "You're all set"."
Then I much prefer the Lord Frederick Roberts origin:
One theory is that the phrase refers to Lord Frederick Roberts (1832–1914. 1st Earl Roberts, Roberts of Kandahar).Roberts was an Anglo-Irish soldier, born in India, who fought and commanded in India, Abyssinia, Afghanistan, and South Africa. Roberts was one of the most successful commanders of the 19th century and was cited for numerous acts of gallantry. His finest hour was perhaps the ending of the siege of Kandahar in 1878, when he marched a force of 10,000 men more than 300 miles from Kabul, winning a battle, and ending the siege. Well respected amongst his men, Roberts was affectionately referred to as 'Uncle Bobs'. Generally meaning 'all will be well', and often used to indicate a successful outcome, the phrase "Bob's your uncle" is said to have been a term originally used by Roberts's men to increase confidence among the ranks and imply that all would be well.
Makes much more sense and, like a lot of these expressions, the phrase always had a British Armed Services connection, particularly Army in this case.