Train Frankfurt to Bamberg

Here's an even cheaper way. Go from the airport regional station on the S-9 to the Hbf and change to a regional express to Kahl am Main. That is just over the border in Bavaria and the fare is 7.60 pp. Then proceed to Bamberg on a Bayern ticket (26 for 2). So that gets you to 41.20 for 2. Oh yes, perfectly valid way to go. It'll take you a little extra time and trouble, 2 extra train changes, buying tickets out of the machine to avoid counter charges, (is there a machine at Kahl station?), trucking around the Hbf locating your connection, slower trains. So its not like your getting something for nothing.
By the way, the fare for going this way to Aschaffenburg is 11.00 pp.

You can buy a Bayern ticket from the ticket machines in the Frankfurt airport, so no need to get off the train in Kahl. You just buy your ticket from the airport to Kahl, and once you pass Kahl, the Bayern ticket becomes valid. You would ride the S-bahn to Frankfurt, get on the regional train to Würzburg and then switch to your train to Bamburg. Total travel time about 3.5 hours.

"What I want to do is book a ticket from Frankfurt Airport-Aschaffenburg HBF (in Bavaria) for 20 euro..." It's possible to book this route in advance for 20€ if you want to pay extra for the high-speed trains. The local/regional train option is 11€; you buy tix at the airport station, not bookable in advance. As Sam points out, Kahl is a cheaper route at 7.60€. Since you'll be buying tickets at FRA anyway, just get the Bayern Ticket at the same time - there's no advantage to buying it in advance. Note that FRA has two airport stations - the Regionalbahnhof, generally for the local/regional trains, and the Fernbahnhof for the high-speed equipment. Will you be taking outings from Bamberg? The local transportation network (VGN) sells a daypass (Tagesticket Plus) that costs 16.80€/day for two adults and will get you from Bamberg to Nuremberg, Bad Windsheim (Franconian open-air Museum,) Rothenburg, Bayreuth, Iphofen, Weißenburg, and other destinations. If you buy it on Saturday, you can use it on Sunday too. www.vgn.de/en/dayticket?Edition=en&p=1

Thanks everyone for the responses. So what I gather is the prices I see on BAHN.DE are for advanced purchase, but are actually cheaper a the station. How do you find that price? I am wondering what the cost for the high speed train from Frankfurt Airport - Bamberg is? The website says 56 euros and about 2.5 hour travel time. Since the cheaper alternative with the Bayern Ticket takes about 3.5 hours I am trying to figure out the premium we would be paying to save the 1 hour. Thanks everyone.

"So what I gather is the prices I see on BAHN.DE are for advanced purchase, but are actually cheaper a the station. How do you find that price?" It's not that purchase at the station is cheaper... it's a little complicated... DB has higher prices for high-speed trains (IC, ICE, EC) than for the local/regional trains. Find the cheaper trains by ticking "only local transport" under "means of transport" on THIS PAGE. Leaving it set to "ALL" will pull up itineraries that include high-speed trains. For FRA airport to Bamberg: on "ALL", you'll get itin's with an ICE or an IC train + 1 or 2 RE, RB or S trains (since not every leg of your journey is served by high-speed trains.) The "standard fare" for any itin. including any high-speed train is 56€ each; you might also see some cheaper "savings fares" (advance purchase, capacity-controlled train/time specific, penalties for changes, forfeiture if you miss your train; problem with these tickets from FRA is that any delay at the airport might mean forfeiture.) Search FRA-Bamberg on "only local transport", and you get only S, RE, and RB trains, longer trip times, and a price of 40.60€ each, 15€ cheaper than the standard high-speed fare. But that's not the whole story. DB doesn't sell all tickets in Germany - local transit authorities sell tickets too. So the reason you can't find the price for FRA-Kahl local trains is that this local trip lies entirely within the jurisdiction of the local transit authority (RMV) and only RMV sells the ticket. HERE is their fare-finding page. In your case, the RMV ticket + the Bayern ticket is cheapest.

Thanks Russ. That clears it up.