If I play Bullet Time do I have to announce how many runes I want to recycle before the card resolves?

No, you do not have to announce how many runes you want to recycle when you play Bullet Time.

According to the official ruling for Bullet Time:

  1. Play Bullet Time: You play the card and choose the target battlefield.
  2. Opponent Responds: Your opponent has an opportunity to react to the spell (e.g., with Defy or other responses) without knowing how much power you intend to spend.
  3. Resolution: Once all responses have resolved, Bullet Time begins to resolve. It is only during this resolution phase that you choose how much power to pay by recycling runes.

Because the power cost is paid during resolution rather than as an additional cost to cast the card, your opponent cannot see how much damage you will deal before deciding whether to respond to the spell. If Bullet Time is countered before it resolves, you do not pay any power and no runes are recycled.