Where can I find the Booking ID within my Stripe account?

You can find this by visiting:

The 'Payments' menu and then clicking 'View all payments'. You'll see "Pitchup.com (Booking ID)" on each row. Click the row to see the full details of the payment
The 'Transfers' menu and clicking the row for the 'Charge' (Balance transaction). The Booking ID appears within the 'Payment Details' box as part of the 'Description'