How long was it between the time you first met and started going out?
この場合、次のような言い方ができますよ。
ーHow long after you met him did you start dating?
「彼と出会った後どのくらいで付き合い始めたの?」
ーHow long was it between the time you first met and started going out?
「初めて出会ってから付き合い始めるまでの間はどのくらいだった?」
ご参考まで!