When you choose "Hide my email", Apple will generate an email address for you (E.g. email@example.com). Apple links this generated email address to the email address used for your Apple ID.
Even if you're unsure what the generated email address is, you can still log in to your Burpple account with your Apple ID by selecting on the login page.
If you want to see the email address that was generated for you, you can do so via the Burpple app when you are logged in (Profile > Setting > Edit Profile > Email).