When is my card charged?

Not when you make the request. When you book, your bank only records a pre-authorisation: a hold that sets the amount aside, with no charge. The money doesn't move until the pilot has accepted.

If the pilot accepts

The payment is then captured: it's at that moment, the moment of acceptance, that your card is actually charged. The funds are then held in escrow until the flight, and the pilot is only paid once the flight has taken place.

If nothing comes of it

If the request is declined, goes unanswered, or the booking is left unpaid, the hold is released and no transaction appears on your account.