You are on the right track.
$connection = (new TicketAPI)->bookings($attributes);
The problem with the above statement is that you are still directly "newing up" an instance of TicketAPI. What you want to do, is something like this:
$connection = resolve(TicketAPI::class)->bookings($attributes);
Or, better yet, look into swapping out your underlying service class by coding them to an interface. When you code to an interface, you can swap out the underlying implementation by updating a single binding (usually within a service provider)
For example:
ServiceProvider:
$this->app->bind(TicketInterface::class, TicketAPI::class);
Anywhere within your app that needs it:
$connection = resolve(TicketInterface::class)->bookings($attributes);
Test:
$fakeTicket = new FakeTicket;
$this->app->instance(TicketInterface::class, $fakeTicket);