“-eth” is third person singular present imperfect, as in “the ice man cometh” or “the lady doth protest too much”

Second person singular present imperfect is “-est” as in “thou shakest indeed thy fundament!”

But this playlist wants second person imperative (command tense), which is simply “shake”.

So “Shake thy bottom” is correct here; if it were a noun starting in a vowel, “thine” is correct, so “shake thine ass, wench!”