Is there public transportation such as bus to get you too French Quarter

Yes, there is public transportation but you will need to speak with the airport staff to see where the information is located. You would basically be using buses to go though three different areas: Kenner, Metairie, and New Orleans. It might be better to catch a cab for 35.00 or see if there is a paid shuttle service for a decent price at the airport.

Air port shuttle service is convenient too

Yes have. E2 Express bus 2.50 $ And RTA bus 1.50$

Yes, but its a pain in the backside. Better off taking a cab.