So you went to BN.com on your HD+ and bought a book. Well, assuming you logged in with the same account you can go to your library on your HD+ and just refresh it, the book should appear as long as you're in WiFi.
Of course you could save yourself that step by going to the clearly labled 'shop' from the homescreen and buying a book from that, which would bring the book directly to your Nook, along with any apps, tv shows, or movies you wanted to purchase.
If you did go through the 'Shop' feature you should see the books image on your homescreen with a cloud above it with a green arrow pointing down. Tap that icon.
I'm guessing you went through the website since you never mentioned the shop but specifically mentioned the site, and you've run tech companies so you would know to be percise with terminology.
I've felt this a lot of times too:
I would FIRE everyone in the product management chain that allowed the critical revenue stream of the company to NOT WORK.
B&N is doing fixes for the HD and HD+. They still have work to do.
It does amaze me that the revenue streams i.e. buying books, buying movies, etc. are not PERFECTLY done by launch (let alone now).
There are some disconnects between website and servers and devices sometimes.
Usually a book that you buy shows up almost automatically on your Nook. For me it always seems to happen with free books that I wish didn't show up automatically.
IN a few rare cases they won't.
Sometimes they appear after a few hours.
Sometimes you have to go to your Nook, then go to the Apps or Library page, and then tap on the sync button.