Train Munich to Passau

The savings to book online now are only 10 euros and the bus ticket still has to be purchased locally, so I'd buy it all there on arrival.

Because you cannot be sure that your plane will land on time I would also buy tickets on arrival.

I understand if buy it at airport I must pay cash and can take any train. If I buy ahead, it costs more and I have to take a specific train.

You can use your credit card. Pre-booking saver fares for long distance trains will be risky (you are bound to a specific trainb and if your flight is late you will have lost your money). Besides, it wont be much cheaper than a flex price ticket. If your departure is after 9am buy a Bayern Ticket for €31/2 from a ticket automat and use local trains / buses only. Example: Take the 9:21 bus 635 to Freising and transfer there to RE 4046 to Passau, arr. 11:36. Total travel time is 2:15, just 2min longer than a later connection involving an ICE and an additional transfer in Plattling.

There are 2 routes from Munich airport to Passau.
1. Airport to Munchen Ost by Sbahn S 8, Then regional train to Mühldorf(Oberbay), change there for Passau
2. Airport to Freising by bus 635, then regional train to Plattling. From Plattling you can either pick up the ICE train, if you paid the higher price. If you are using a Bayern ticket, then currently there is a replacement bus service from Plattling to Osterhofen, then regional train for remainder of journey

https://www.bahn.com/en/view/index.shtml
https://www.bahn.com/en/view/offers/regional/regional-day-tickets.shtml?dbkanal_007=L04_S02_D002_KIN0060_NAVIGATION-LINKS-REGIONALE-TICKETS_LZ01
https://www.bahn.de/p/view/angebot/regio/regionale-tickets/bayern/regio-ticket-donau-isar.shtml
https://www.bahn.de/p/view/angebot/regio/regionale-tickets/bayern/suedostbayern-ticket.shtml

An advance purchase, SparPreis-Ticket (Savings-Fare) has to include at least one leg with a long distance train (IC/EC/ICE). Such a route will cost you more, only save you about 20 minutes, and will commit you to a specific train. Unless you have a BahnCard (not practical for most US visitors) you will have to pay for the bus separately. The fare would be 2,80€ for the bus and at least 29,90€ for the Bahn ticket, so 32,70€, total. If you had the SparPreis-Ticket in hand when you arrived, you could buy the bus ticket from the driver. The total trip takes 2¼ hours, plus or minus a few minutes.

You can use a regional or Länder fare for this trip. The absolutely least expensive fare would be to purchase your bus ticket (2,80€) from the driver and a Regio-Ticket Donau-Isar at the airport for 20,-€ (22,80€ total). You could also buy the Regio-Ticket at the Freising Bhf, but the bus is scheduled to arrive at Freising Bhf 9 minutes before the Regional Express (RE) leaves Freising for Plattlling, so you would have to know exactly what you were doing. The bus runs every 20 minutes, so if you caught the earlier bus (at 9:01, you would have 29 minutes to buy you Regio-Ticket at Freising and catch the 9:48 RE. The bus ticket is valid anytime for that price so you could leave the airport for Freising at any time, but the Regio-Ticket is only valid after 9 AM workdays, so you couldn't leave Freising until 9:48.

A Bayern-Ticket for 25€ would include the regional trains to Passau plus any conveyance of the MVV so you would not have to purchase the bus ticket separately. You used to be able to purchase the Bayern-Ticket from the bus driver; I imagine you still can, but don't try to give him a big bill. The Bayern-Ticket could not be used for the bus before 9 AM, but if you leave the airport on the 9:21 bus, you would still catch the 9:48 RE.

Use the German Rail (Bahn) schedule webpage for schedules. Use "München Flughafen Terminal" for from: (use "ue" for ü, the website will change it for you) and Passau for to:

I looks like they are currently working on the tracks between Plattling and Osterhofen. You'll have to use a substitute bus (SEV) around the work.

I have done just what sla019 said:

"If your departure is after 9am buy a Bayern Ticket for €31/2 from a ticket automat and use local trains / buses only. Example: Take the 9:21 bus 635 to Freising and transfer there to RE 4046 to Passau, arr. 11:36"

The Bayern ticket covers the Bus & train after 9:00 AM on weekdays. If you are before 9:00, then the bus driver can sell you a ticket to the Freising train station where you can wait till after 9:00 and use a Bayern ticket from there.

Check schedules:

http://reiseauskunft.bahn.de/bin/query.exe/en