The booklet feature really has no connection with the book panel, so it won't get you where you're trying to go. It was intended for short booklets that someone would print on an office printer, which as a matter of practicality are usually single documents not more than 20-24 finished pages.
The book panel is for longer publications (hundreds of pages). These become very unwieldy, not to mention hard to farm out for editing and proofing, if they're all in one file. Any printing or export of a book must be done from the book panel flyout menu. The regular File > Print and File > Export menu items only apply to whatever individual document has focus at the time, not to the book. An InDesign document doesn't “know” (has no metadata that indicates) it is part of a book. That information is in the .indb book file.
What you can do, if you have Acrobat, is output your book from the book panel as a single PDF, then use Acrobat to print the booklet. Open the file in Acrobat, select File > Print, and then the fun starts.
“Booklet Printing” is, wierdly enough, one of the “Page Scaling” options. I guess they just didn't know where else to put it. Once you select that, an new button shows up labeled “Booklet subset” that lets you choose to print All the sheets — only useful if you have a printer that can print both sides in a single pass — or a subset (fronts only or backs only). You'll have to experiment with your printer to find the setting that works for you. Look under “Printing – Other ways to print PDFs” in Acrobat Help for more info.
If you need to end up with a PDF that is already set up in printer spreads, print from Acrobat as above, but to the PDF printer.