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Origin documented
“A mile and a bittock”
What it means
Considerably further than you have been led to believe.
Where it comes from
A bittock is a Scots diminutive meaning a little bit. The joke is that the mile in question is a Scots mile of 1,976 yards, already longer than the English one, and the bittock is doing a great deal of quiet work on top of it.
How sure are we?
Well attested in Scots usage, and Robert Louis Stevenson uses it in Kidnapped. The phrase is a warning dressed as reassurance, which is a very Scottish construction.