I researched the same question and you have two basic options, all trains or bus & train:
Via rail: S1 towards Munich hbf, exit at Neurahrn
S1 north to Freising and exit at Freising S1 and go to DB platform 4 for train to Regensburg.
Via bus to Freising & train to Regensburg:
Regionalbus 635 to Freising. Walk 4 minutes to the train station platform.
Use the MVV (metro rail) Planner to look at your likely itineraries:
The Lander Ticket for Bavaria covers all these connections.
For sure, the best way is to just take the 635 bus to Freising. It's only 15 minutes at the most and then you can catch the train to Regensburg with ease. It's best not to try the Neufahrn drill, it's a charley-foxtrot. The bus is only about €2,30 each unless you have the Länder-Ticket. From there it's only about a 1 hour ride to Regensburg. Great place to visit.
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