I really think you can read that both ways. Getting bored of denying it may mean just that. He's bored of being asked and having to repeat ad nauseum.
Or it may mean he's bored because it's true and he wants to scream it out loud and proud!
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist