After a minute on Google I found a solution, using Dropbox, which I access from my computers and my iPad.
- On your computer put the .mobi e-book file in your Dropbox folder and wait for it to sync.
- Then go on your iPad, open Dropbox and then click on the e-book file. The Dropbox app cannot read the file and asks you what program you want to open it with. Select the Amazon Kindle app, and it'll download the book to the the Kindle apps local data store.
It would be nice if Amazon would let you leverage their Cloud Drive free online storage space for Kindle-format books purchased elsewhere, and then let you access it from the Kindle app on the iPad.
Apparently, e-books from Webscriptions.net are available in a format supported by Apple's iBook app, and to which you can add them using iTunes. Clicky here.