I advise you to have an internal channel of communication between the microservices.
For example, using some message broker like RabbitMQ internally to send/receive or publish/subscribe messages between the microservices.
Then your end-user facing service "in your example the Booking service" will be responsible for validating the token and authorizing the customer to do this specific operation "maybe by communicating with IdentityServer".
Then it will communicate with the "Services" service through the Message broker. In this case, there is no need to validate the token again.
I guess this model will be simpler and give you a better performance.