In order to share your iPad or iPhone screen during a BigBlueButton session, you must first also have a Mac on hand.
On your Mac, follow the steps in this article to share your iPad/iPhone screen to your Mac.
Once that is done, you can then share the iPad/iPhone screen in the BigBlueButton session by clicking the "Share screen" button.
This will bring up the Screen Share menu.
Once in the Screen Share menu, click Window  then select the Movie Recording  window which will be your iPad/iPhone screen. Finally, click the Share  button.
The rest of the session will now see the iPad/iPhone screen.