Can I play Hard Bargain even with nothing on the stack?

No, you cannot play Hard Bargain if there is nothing on the chain.

According to the rules of the game:

1. Targeting Requirements: Hard Bargain requires a target ("Counter a spell..."). To play a card, you must be able to choose a valid target at the time you place the spell on the chain. If there are no spells on the chain, there are no valid targets for Hard Bargain.
2. Playing Cards: Rule 358.1 requires that you check that all chosen targets are legal when you play a card. If you cannot choose a legal target, the action of playing that card is illegal and will be cancelled (Rule 358.4).

While Hard Bargain has the [Reaction] keyword—allowing it to be played at times other than just when it's your main phase—it still requires a legal target to be played. Since a "spell" must be on the chain to be a target, an empty chain means there is nothing to target, and therefore you cannot play Hard Bargain.