I have a good picture of how to implement such a booking calendar for you.
My plan is to setup the framework and come up with the basic UI for the calendar. If you have the wireframe it would be great.
After the basic UI and framework are done we can start to implement the business logic that you need and some user interaction with the UI.
With this cost, I assume that you only need a very simple UI with mentioned functionality. Potentially enhanced and add-on features would involves more cost
Please contact me if you have any questions. Look forward to working with you
Regards,