I read earlier and and can't relocate that someone suggested bus from munchen airport to Freising and train to Regensburg. Where do you buy that ticket?
If you are by yourself and won't do any more traveling that day, you can buy your bus ticket (2,60€) from the driver on the bus. Then, buy your ticket from Freising to Regensburg (18,60€ at the automat or ticket counter) in the station at Freising. If there are two or more, a Bayern-Ticket (26€ for two) will cover both the bus to Freising and a regional train (that's all I see for for the trip) for Freising to Regensburg. If you have exact change, I think you can buy the Bayern-Ticket from the bus driver, but for sure you can buy it (at an automat or, for 2€ more, from the DB ticket counter) in the Munich Airport Center above the S-Bahn station between the terminals.