You can buy Airbus tickets online through the website of any airline that flies the Airbus, including American Airlines, United Airlines and Delta Air Lines. Search for flights using the airline's online search tool, and click Details in Flight Information for each available flight to view the aircraft's name.
When you book a flight ticket online with an airline, you search for a route rather than a specific aircraft. However, as U.S. airlines have purchased more than 2,000 of the aircraft, as at 2015, there is a reasonable chance of flying on an Airbus. American Airlines flies the Airbus A330 and A321; United Airlines flies the Airbus 319 and 320, while Delta Airlines flies the A319, A320 and A330. The Airbus A319, A320 and A321 are narrow-bodied jets that fly short-haul and domestic routes within the United States, while the A330 is a wide-bodied jet that flies International routes.