At which point in Bullet Time do I pay the power, can my opponent choose to play a reaction first before I pay the power cost?

According to the official rulings for Bullet Time:

When do you pay the power?

You pay the power cost during the resolution of the spell, not when you cast it. The total cost to play Bullet Time is only its base energy cost (1 energy). The amount of power you choose to pay is determined and paid only when the spell resolves.

Can your opponent react before you pay?

Yes. The sequence of events is as follows:

1. Cast: You pay the 1 energy cost and place Bullet Time on the chain.
2. Reaction Window: Your opponent receives priority and may play reactions (such as Retreat or other spells with the Reaction keyword) while Bullet Time is on the chain. Crucially, your opponent must make these decisions without knowing how much power you intend to pay.
3. Resolution: After all reactions on the chain have resolved, Bullet Time begins to resolve. At this point, you choose how much power to pay and deal that much damage to all enemy units at the chosen battlefield.

Important Nuances:

• No Reaction Window After Payment: There is no reaction window after you pay the power during resolution. Once you begin the resolution process and pay the power, the damage is dealt immediately.
• Countering: If your opponent plays a card that counters Bullet Time while it is on the chain, the spell is negated and sent to the trash before it resolves. In this case, you do not pay any power.
• Resource Generation: Per RiftJudge FAQ #5521 and #1771, you are permitted to use reaction-speed "Add" abilities (such as exhausting or recycling runes) during the resolution of Bullet Time to generate the power you need to pay.

This ruling is based on RiftJudge FAQs #5653, #8161, #4766, #5521, and #6241.