Emails come from the Book Like a Boss booking platform at this time but you are able to edit the "Reply To" email address so that when your clients reply to an email it goes to another email address, aside from the email address that has been used as the login for the BLAB account.
The Public Email Address which is found here https://bookme.name/account/profile is for setting the Reply To address to something other than your Book Like A Boss login email address.
To change the Reply To email address go to your Profile Details and enter the preferred email address in the Public Email Address text box.