Who played the twangy part (bass?) on Nancy Sinatra's "These Boots Are Made For Walking"?

Answer 1

per Wikipedia:

Sinatra was encouraged by Hazlewood to sing the song as if she were a sixteen-year-old girl giving the brush-off to a forty-year-old man. Sinatra's recording of the song was made with the help of notable Los Angeles session musicians known as the Wrecking Crew. This session included Hal Blaine on drums, Tommy Tedesco and Billy Strange on guitars, Ollie Mitchell, Roy Caton and Lew McCreary on horns, Carol Kaye on electric bass, and Chuck Berghofer on double bass, providing the notable bass line.

According to Carol Kaye, "Arranger Billy Strange believed in using the two basses together. Producer Lee Hazlewood asked Chuck to put a sliding run on the front of the tune. Chuck complied by playing notes about three tones apart (4-6 frets apart), but Lee stopped the take. "No Chuck, make your sliding notes closer together", and that is what you hear."