Just one bit of info to clarify, because I got confused when I read your instructions (problem is me)
Try this:
1.Launch iBooks app.
2. Tap My Books at the bottom left corner
3. Tap Select from the upper right corner
Good so far here is my change:
4. Tap the icon of the book you want to delete.
Small thing, but I got confused. So in case anyone suffers from my kind of confusions.
5.When you tap on Delete, you have options – Delete and Delete This Copy.
If you tap Delete, your books are removed from your phone but they will still be visible in Purchased section. If you tap Delete this copy, they are still visible there with the iCloud icon. They won’t take space on your device but you can download them from there only instead of going to Purchased.
If you have synced your books with all your devices registered with the iCloud account (Settings → iBooks → Turn on Sync Collections)you will see another option Delete from All Devices. When you tap it, your books will be deleted from all iOS devices.
Hope this will help
All in all very excellent instructions. Thank thee so muchly.