I can't help with the equivalent French expression, but in English it's used in different ways. "Quit busting my hump" could mean "stop nagging me about this" or "stop criticizing me constantly" or "stop punishing me".
If someone uses it about themselves ("I've been busting my hump") it usually means I've been working extra hard or working for long hours.
It is never "burst," but instead "bust," since this second form is the colloquial one. "Quit bustin' my hump" means "quit giving me trouble" or "stop giving me a hard time." It's used very informally. An example: If someone always teases you and makes fun of you, you can say "Quit bustin' my hump!" Be careful, though, because it's a little vulgar.
Un bon équivalent serait: "Arrête de me casser les couilles."
Qui est un chouilla plus vulgaire en francais...
En passant l'expression "busting my balls" existe aussi, mais le sens peut être plus proche de "se casser la tête (à faire quelquechose)" selon the contexte.
"stop busting my balls" => "arrête de me prendre la tête/casser les couilles"
"I've been busting my balls (to do something)"=> "je me suis cassé la tête (à faire quelquechose)"
I agree with you entirely Randisi, but I'm not entirely sure I see your point.
I agree that in the form "I've been busting my hump (doing something)" the hump refers to the back and that this expression means having worked hard at something.
The original (and probably long gone) poster's question pertained to the form "quit bustin' my hump", and the commonly used french equivalent as I said in previous post is "arrête de me cassser les couilles" or "arrête de me prendre la tête", which is admittedly more vulgar in french than the English (which as you pointed out isn't really vulgar at all, but merely colloquial) but they are very much used nonetheless... perhaps even more commonly used than "quit busting my hump" is in English.