Bobbie was Judy's on-screen double. Caren was Judy's stand-in (never on screen).
Caren was a necessary part of the equation, largely because Judy was a minor, under strict child labor laws. It was Caren who learned all the blocking for the Munchkinland sequence and worked with everyone while the Munchkins learned their steps, etc. Long hours. Then when they were ready for a take, Judy would step out of her trailer, Caren would show her the blocking, and Judy would do it once or twice for the cameras.
Caren also spent a long time working on the tornado sequence. They tested the power of the wind machines, the lighting, blocking, etc., on Caren (fully costumed as Dorothy) until they got it just right ... then Judy stepped in for the filming.
Bobbie is actually on screen several times in the film. She was Judy's "stunt double" as well as double. It's Bobbie who snags her foot on a wire and falls into the pigsty. It's also Bobbie that's lifted up into the air by the flying monkeys.
And in my favorite unedited shot in the movie, it's Bobbie (wearing a B&W checked dress) who opens the door into Munchkinland with her back to the camera, then backs off screen and hands Toto to Judy, who then walks through the door in a color dress into Munchkinland.
"Jaws is the Citizen Kane of movies."
blocked: logan2, Diamonds3, Hamilton22