Just to clarify to make sure we’re on the same page, when you say you signed up through WordPress are you saying that you installed the BoldGrid plugin through the WordPress Dashboard plugin area? Or, are you saying you went through a formal sign-up process?
To answer your question, no you are not required to purchase a premium key. You can request a free key to unlock the base feature set. If you did not receive key after requesting one, I’d advise checking your spam folders to make sure the message was not classified as junk. Once a key has been added the pop-up will cease to show up in WordPress and you may continue to use BoldGrid as intended.