The James Bond novels, from which the films take their inspiration, were created by Ian Fleming from 1953 onwards. In the early novels (starting with Casino Royale) he doesn't give Bond much background, but by the end of the series he had given him a Scottish background. The last book but one, You Only Live Twice, tells us that Bond is the son of a Scottish father, Andrew, and a Swiss mother, Monique, and that he grows up in Skyfall Lodge in the village of Glencoe, attending the famous Scottish public school, Fettes. Tony Blair attended this school, and ironically enough it was on Sean Connery's round in his early career as a milkman.
You Only Live Twice was published in 1964, when Connery had already become famous as the screen Bond, so it is possible that the idea of giving the character a Scottish background came from Connery's performance.
Fleming's original inspiration for James Bond came from real-life British spy Sidney Reilly, who was actually born in Russia.