It's not bonnie but it's the only blue bonnets I know - blue bonnets over the border

Chorus:
March! March! Ettrick and Tevot-dale,
Why my lads dinnaye march forward in order
March! March! Eskdale and Liddesdale!
All the blue bonnets are over the border

Many a banner spread,
Flutters above your head,
Many a crest that is famous in story,
Mount and make ready then,
Sons of the mountain glen,
Fight for your King and the old Scottish border.

Chorus

Come from the hills where your hirsels are grazing,
Come from the glens of the buck and the roe;
Come to the grag where the beacon is blazing
Come with the buckler, the lance, and the bow

Trumpets are sounding,
War steeds are bounding.
Stand to your arms and march on good order
England shall many a day,
Tell of the bloody fray,
When the blue bonnets came over the border

Chorus

(from a broadside circa 1820/1830)