How to print Apple photo books from my Mac?

If you're running Photos 4.0 there should be a button in the right hand corner to create a PDF of the book:

Once you're created the PDF file you can upload it to PrestoPhotos for printing and binding. There have been a number of users who have used their service and reportrf back with favorable comments about the finished product.

Or you an use one of the extensions available to create a new book: Post 9/30/2018 Printing Options for Photos. Mimeo has a convert option to convert the current photo boot to their format:

Any time you use something like that be sure to duplicate the book and run the duplicate thru the converter.

Third party company, like following one could help your project.

Create Photo Books | Make Your Own Photo Book | Collage.com

Unfortunately, I don't think that there is any way to have the book that you have already created printed since they have stopped offering that service.