But, Laura, Munich to Füssen takes longer, 2 hours, and half the time there is one change of train, usually at Buchloe. Munich to Oberammergau take less time, 1 hour 45 min, with a change at Murnau.
The complete bus schedule between Oberammergau and Füssen (RVO 9606) is here. The bus schedule between Oberammergau and Linderhof (RVO 9622) is here.
There is a bus leaving Oberammergau at 6:40, getting to Linderhof at 7:05. Linderhof doesn't open until 9; you don't want that one. The next bus is at 9:30, getting to Linderhof at 10:00. There are buses leaving Linderhof at 10:50 and 12:00. The 12:00 bus (giving you 2 hours at Linderhof) gets to Oberammergau Bahnhof at 12:24 on school days, 12:29 on non-school days. There is a bus leaving Oberammergau at 12:50, changing at Echelsbacher Brücke, getting to Füssen Bahnhof at 14:51, 14 minutes before your 15:05 trains.
But, if you are staying in Oberammergau, why go to Füssen to catch the train to Munich (the 15:05 train gets to Munich at 17:05). There is a train leaving Oberammergau at 14:39, giving you more time to get your luggage at the hotel, and getting into Munich at 16:26, half an hour earlier than the train from Füssen).
If you go to Munich from Oberammergau, you could stay at Linderhof until 12:50, get back to Oberammergau at 13:09, still with plenty of time to catch the 14:39 train to Munich.
If you are staying in Oberammergau, I would recommend Gästehaus Richter. It's a nice place, good price for Oberammergau, Frau Richter is gracious and speaks good English, and it's about a block (220 m, 3 min walk) from the train/bus station in Oberammergau.
If you are staying both nights in Oberammergau, you can make reservations in advance on the Hohenschwangau website, take the bus in the morning to Hohenschwangau and pick up your tour tickets at the kiosk, tour both castles, and catch the last bus back to Oberammergau at 17:10.
All of this assumes weekday travel. The buses on weekends run less often.