There are trains to Oberammergau with a change in Murnau. At the Oberammergau Bahnhof you can take a bus, 9622, about 15 minutes to Linderhof. Here is the schedule. Then there is a bus, 9606, from Oberammergau to the Hohenschwangau bus stop, schedule here, just down the street from the ticket kiosk for Neuschwanstein. After Neuschwanstein, come home from Füssen to Munich on the train. If you do this on a weekend day, the entire trip, train and buses, will be covered with a Bayern-Ticket and you can leave from Munich earlier than 9 AM. If on a workday, you can leave Munich Hbf on the 8:32 trains with a 3-zone MVV ticket for 8,40€/adult. That ticket takes you to Tutzing at 9 AM, from where you can use the Bayern-Ticket the rest of the day.
There is one problem with trying to see Linderhof and Neuschwanstein in a single day. Although the palace at Linderhof is quite small and admission is limited to guided tours that last about 25 minutes, but the rest of the grounds are openly accessible (the Grotto is also accessible only by tour). The grounds are very extensive. I spent about six hours total at Linderhof. That would not have left enough time for Neuschwanstein, too. To see both, you would have to leave Linderhof without seeing the whole thing.
