Our first Damsel in Distress is Claudette Colbert. She had a brief scene in the opening sequence of her movie The Palm Beach Story.
She is sitting in the closet with her hands tied behind her back and she is gagged with a thick towel (or maybe a sweater) tied over her mouth. Her legs are free and that's why she manages to kick her way out of the closet.
The video is 1:24 long because I left there almost the whole opening segment, not only the bondage.