To get the best results from the Book Fold option in Word, it is perhaps advisable to set the conditions required first before any content is added. This helps prevent formatting issues that you are experiencing.

My example will be using A4 default blank document and the printer I’m using is the type which prints one side at a time, not a duplex/print both sides printer.

Open Word with a blank document on view.
Click the Page Layout tab and then expand the Page Setup options.
In Margins, set the Multiple pages to Book Fold. This turns the A4 document to Landscape where the 2 A5 sized pages are automatically added.
Now set your Margins, then the Gutter size.
The Gutter is where the pages are stitched, glued, stapled ext.

The showing page, as well as any added, is now in the correct ‘condition’ for added content.

When your pages are finished (I've used 4), go to the Print settings by your usual method.
In the Settings, click the Print One Sided tab, then the Manually Print on Both Sides.
Clicking the Print tab will print out an A4 sheet with pages 1 and 4 (front and back).
An advisory dialog box should pop up telling you to remove the sheet (when printed) and to put back in the printer tray upside down and in the correct orientation to then print the remaining pages (2 and 3) on the reverse of what has just been printed.

When the pages are put together and folded, in this example, you get a 4 page document sized at A5.
Using 6, 8, 10, 12 pages etc is the same.
Click the image below to see a short video showing how I have done this.