You could do it all in Bubble which would save you the trouble of maintaining 2 databases, but no reason you couldn’t use both if you wanted Airtable for something specific they offer.
For the scheduling portion, you might want to checkout my template and plugin.
For payments you will probably want to use Stripe for card payments, but if you need an in store payment system to be connected to this system not sure the best route for that, probably another system with a good API