If Bonnie is Princess Leia, Clyde is Han Solo, Buck is Chewbacca, and C.W. is R2D2, then Blanche is…C-3PO.
She's nervous. She's insecure. She's sometimes hysterical, and becomes unhinged when violence goes down. Sure, she doesn't have C-3PO's English butler-like mannerisms, but she's just as uptight.
A preacher's daughter, Blanche married Buck when he was a reformed ex-con. We get the feeling that this reformation was exactly what attracted her to Buck—unlike Bonnie, who was attracted to Clyde's lawlessness.
BLANCHE: Oh, lord.
C.W.: Why don't you go back to your Pa's house?
BLANCHE: If I only could. If I could only just do that one thing. There's no telling how all this happened. I was a preacher's daughter! […] He thought the world of Buck, my daddy did. Even though Buck was serving time in jail. He forgave him because he paid his debt to society.
We feel sorry for Blanche; she's in over her head. But Bonnie hates her. They're polar opposites: Blanche is dowdy while Bonnie is glamorous. Blanche is nervous while Bonnie's a free spirit. But what really gets on Bonnie's nerves is Blanche's desire to take a cut of the earnings from the robberies.
Ultimately, Blanche is blinded by a stray bullet and left behind to tend to the body of her dead husband. The police apprehend her, and use her to find out more about the Barrow Gang.
The last time we see Blanche, he head's wrapped in white bandages. She breaks down in tears and gives the police as much information as they want. She also starts to tell her version of the story:
BLANCHE: I didn't want to go. I didn't want to. And Buck said we was just going on a visit, and we wouldn't do no stealing or robbing. And we went up to Joplin all of a sudden. And all of a sudden they just started shooting…
But the cop questioning her walks out of the room as she's talking. He shuts the door to her cell and her words are cut off. That's the last time we see poor Blanche Barrow.