I think you're asking about The Accidental Sorcerer, by K E Mills
From the Amazon.com summary:
Gerald Dunwoody, a Third Grade wizard and lowly safety inspector for Ottoslands Department of Thaumaturgy, inadvertently blows up a factory while trying to save it. Summarily fired, Gerald takes a job in almost bankrupt New Ottosland as royal court wizard for King Lional the 43rd. To prove his powers to the doubtful king and his put-upon sister, Prime Minister Princess Melissande, Gerald turns a cat into a lion and transforms the dowdy princess into a literally bewitching fashion plate, but preventing war between New Ottosland and Kallarap and making a highly illegal dragon for the king may be beyond his will and abilities
It's been a while since I read it, so I can't remember anything about the magic bird, but it matches the rest of what you recall.