To publish a new version of a book in the Bring Your Own Book writing mode, you just need to upload a new book file, and that will automatically replace the old one.
To send "Release Notes" about the new version of your book to readers for a book published in the "Bring Your Own Book" writing mode, you need to go here:
...making sure to replace YOUR_BOOK with your book's unique web address.
Please note you shouldn't use the "Release Notes" option very often! This is meant only for major updates.