…there is no 100% right/wrong way to send a booking email, but the best thing you can do for yourself is to make it was easy on the person reading as possible. Be cordial yet brief & honest, and have links readily available in your email. If they like your music the rest is easy, so just make sure youre spending the time in the most beneficial part of your marketing: making good music! And the rest will follow.
https://wordkrapht.com/main/2012/11/22/kraphtsman-guild-tips-from-a-booking-agent/