Name the places you work from — your studio, a partner venue, mobile visits — then say which services happen at each and which practitioners work there.
Appointments → Services → "Locations" → "Add a location". Give it the name your clients would use, then say what kind of place it is: your own space (a room you control), somewhere else at a fixed address (a partner venue, a residence you hold the account for), or wherever the client is (mobile visits). A fixed place can carry an address, which goes on the confirmation email; a mobile one cannot, because the address comes from each booking.
Leave "Show it on your booking page" on for a place a client picks themselves. Turn it off for a place you book into on their behalf — you still see it everywhere in the back office, it simply is not offered online.
Open a service and tick its locations under "Where it happens". Tick nothing and it is offered everywhere, which is how every existing service starts. This is what separates your booking page: a client who picks Mobile sees only the mobile services, and a client who picks your studio sees only what happens there.
Once you have two or more locations showing on your booking page, the page starts with a "Where" row — Anywhere, then each place. Picking one narrows the services and the practitioners to that place, and the booking records it, so the confirmation email says where to come. With one location or none, nobody is asked: there is no choice to make.
Open an instructor → Overview → Details → Edit → "Where they work". Tick nothing and they are offered wherever their services are — so adding locations never quietly removes someone who was bookable yesterday. Tick places and they are offered only there.