I just think it's an idiom and no need for the context.
Okay, here is the full context:
"Cryin' all night in a bucket," she groaned and her breathing quickened. "I can't believe it. I just can't believe it."
"Are you going to get sick?"
"I don't think so." She shook her head and gulped air into her lungs. "But I can't breathe."
Georgeanne left her old rich groom at the weeding, who she is not in love with. Miserably, she is in a stranger's car, and left her friend alone at her groom's house, and telling the stranger about her bad wedding and her friend left behind.
Interestingly enough, I was looking for the meaning of "cryin' all night in a bucket" when I found this topic in a search. The same context, too. But I think Moon & Sun didn't provide enough context. The girl in the book was in a confusing, rather hysterical state when she ran away from her own wedding. The dialogue below happened in a car with the one who just accidentally gave her a lift:
The guy: "Where do you live, Georgie Howard?"
The girl: "Mc Kinney"
The guy:"Is that just south of Tacoma?"
The girl: "Crying all night in a bucket," she groaned, and her breathing quickened. "I can't believe it. I just can't believe it."
Like M&S, at the beginning I thought "Crying all night in a bucket" was a fix expression. But it seemed you native speakers claimed negative. So my wild guess is that it may be an exclamation, like "Oh my God" or something like that. Or, is there any chance for it to be the subject omitted form of "I've been crying all night in a bucket"? This girl was so confused she didn't care about what the guy said, she simply said what was in her mind to herself?