Bashful girl, they say, this Indian (8)

I believe the answer is:

cheyenne

'this indian' is the definition.
(Native American)

I don't understand how the rest of the clue works.

(Other definitions for cheyenne that I've seen before include "N. American people; Wyoming city" , "Wyoming state capital" , "US state capital" , "North American native" , "Indigenous Indian" .)

I've seen this clue in The Times.

Want a hint initially instead of a full solution? Install my app