Neuschwanstein Castle & Bavaria Weekend

To see the outside of the castle would probably take a gentle 3 hours - you have to park at the bottom of the hill and walk up it (or overpay for the horsedrawn carts to haul you up). I didn't bother with the inside of the castle; I've heard it's not that wonderful, but outside definitely is, especially if you continue up past the castle to get to the footbridge for the classic view of the castle overlooking the valley.

The whole area is extremely pretty and there's plenty to do; Munich could easily last you 3 days on its own (1 for the castle, 1 for Dachau, 1 for a quick spin round Munich itself).

Agree with fwoggie, you'll look at about 3 to 5 hours (including your visit inside)
When I was there, they had a shuttle bus going up to the place where there is
a suspension bridge overlooking the castle from above.

But I was inside the castle with a guided tour (looks like that's the only way to visit)
and it's quite nice. The best way is to book your ticket in advance through their
official homepage, then you have a pre-booked timing for visiting the inside.

Good idea to make a pre booking. In this case you pick up your tickest latest one hour before visiting the castle inside. It's naely the time you need to go from their office to the entrance. The time inside is limited to 30 minutes and as written before, there is not a lot to see. http://www.neuschwanstein.de/englisch/tourist/index.htm

Without traffic it's a 12 hour ride round trip, but my guess you'll need around 8 hours to reach Fuessen from Prague riding a bike, at least that is our experience when traveling by bike that it takes a lot longer than by car.

Prebook your tickets as others have suggested, than you can visit the castle early and get back on the road.

If Innsbruck and Oberammergau are not to important I have a nice route http://www.deutsche-alpenstrasse.de/en/home/ you can take it from Fuessen going back towards home, since school vaccations start late in Germany this year I don't think you have to pre book accomodation if you choose to take the alpine road.

Drive save and have an awesome trip.

Seeing as you have your own transport, you can take a ramble round by pretty Oberammargau on the Sunday and a personal tip would be to drive your bikes up Kogel Hill, overlooking the town, and treat yourselves to a meal and drink in the pretty Alm overlooking the valley and enjoy the gorgeous views, thereof...I'd forget about Innsbruck in that timescale and if you have time visit Linderhof Castle and gardens, and maybe Wieskirche Church and Ettal Abbey, instead...also the option of a stop-off at Andechs Monastery on your way back to Munich...