Hmmm... seems like a not-too-bad translation of "bite me", although I'm not sure if the Russian syntax is quite correct in this context.
Although I think that Плевать мне на тебя might be a little closer to "As far as I'm concerned, you can bite me" -- in other words, expressing indifference more than active hostility. Literally, I would interpret Плевать мне на тебя as something like "I'm inclined to spit on you" (or, as Monty Python said, "I fart in your general direction"), as opposed to the very direct Плюю тебе в лицо!, "I spit in your face!"
By the way, for Russians, I would explain "Bite me!" as being a milder (but still rude) euphemism for "Suck my c*ck!" -- not in the literal sexual sense but with the meaning "Go to f*cking hell." So perhaps "Пошёл на баню!" would be a good way to express the euphemistic quality of "Bite me!"