From Brewer's Dictionary of Phrase and Fable:
"Bob's your uncle. Everything will be easy once you have done this. The phrase is said to have been occasioned by A.J.Balfour's promotion by his uncle Robert (Lord Salisbury), the Tory Prime Minister, to the post of Chief Secretary for Ireland. Balfour had previously been made President of the Local Government Board in 1886, then Secretary for Scotland with a seat in the Cabinet. The suggestion of nepotism was difficult to ignore."
P.S. My kids have an uncle Bob.