"The Blues" was (and is) the nickname of the Royal Horse Guards, one of the most senior cavalry regiments in the British army. The name derives from their blue uniforms.

The regiment merged with the Royal Dragoons in 1969 to become "The Blues and Royals"; together with the Life Guards they make up the Household Cavalry. The Blues were especially favoured by George III. The Duke of Wellington was appointed as their Colonel in 1813.

Their officers were exclusively drawn from the aristocracy and gentry and would have come from a moneyed background. In army terms this is socially about as good as it gets and very glamourous indeed. So JA is using "The Blues" as a shorthand for military glamour, wealth and social status. As Mary and many other people would see it, a humble country parson would be nothing by comparison.