Does their spell go to the bottom of the deck still if opponent plays Star Crossed with Fizz and I Hard Bargain?

Yes — either way, the Star-Crossed ends up on the bottom of the deck.

Fizz's "Then recycle it" is a replacement effect that kicks in whenever that spell would leave the chain, for any reason — including being countered (FAQ #10401, #11158). So if your opponent declines to pay the [2] and Hard Bargain counters the spell, it's recycled to the bottom of the deck instead of the trash (exception to Rule 425.1.a). If they do pay [2], the spell resolves and is then recycled anyway. The only difference is whether the bounce effect happens first.