It's quite possible to lure the child slaver out to her death by bringing Bumble outside from Little Lamplight. This does not seem to make other Slavers hostile towards you. You suffer no Karma loss and since the 'necklace' is never placed on Bumble, Bumble will say "I don't like outside. I'm going home", and return to the caverns.
Killing the child slaver before luring Bumble or any other young child from Little Lamplight will turn all slavers hostile towards you. However, drawing nearby super mutants to her, and letting them kill her will not.
Killing the child slaver after luring Bumble or any other young child from Little Lamplight will turn all slavers hostile towards you. Bumble will run back into Little Lamplight and stay there with the slave collar on.
Once Bumble and the child slaver reach the child slave house in Paradise Falls, the slaver is disabled and disappears from the game while Bumble somehow returns to Little Lamplight, still wearing the slave collar.