He started it !

You're correct, young lady, the judge did start it.  But you see, he was holding  all the cards.  You had committed a crime and he was doing his job.  His role is to determine your immediate future; your role is to act remorseful and respectful, though neither emotion may not necessarily be heartfelt.  The judge's duty is to dispense justice in a fair and impartial manner, according to his professional discretion.  He did step out of bounds when, after so administering in your case, he punctuated his ruling with a cavalier "Bye, bye."   But the two of you are not on an equal footing; he is not one of your peeps, so you were treading on shaky ground when you replied "Adios."   So he started it, you hit back, and then the big guns came out and the game was over.  You broke all the rules of wordplay with obscenity and gesture, and will suffer the consequences.  You may or may not learn from your experience, and become a better citizen for your jail time.  The odds would unfortunately seem to be against it. The odds are even greater that the judge will not realize that he should dispense justice with the repsect due his position, and not add casual, snarky remarks to his decisions.  Bye, Bye!