The Booking Form - as constructed in wordpress.com
When I attempted to emulate this I realise that it was a lot of work!
Still, there was a version of the Booking Form on the Belchamp Walter Village Hall website. Thus form was also adapted for event booking such as Bel-fest, Film Club, Valentines etc.
Using a Plug-In - or third-party booking
When searching for help on the construction of forms it is more likely to find.