Getting out to Hohenschwangau with the train and bus is no big deal. There are hourly trains. Every other train is direct, no change. The alternate trains have one change, at Buchloe. It's a cross platform change, and the other train is sitting there waiting for you when you arrive. The train goes to Fuessen Bahnhof. From there you take a bus to Hohenschwangau. The bus leaves from the other side of the station parking lot, a few yards from the front door, and lets you off around the corner from the castle ticket kiosk. One €28 ($40) Bayern-Ticket covers up to five people for all of their travel, including the bus, for the day. (If you want to leave on a workday on the 8:52 train, you must also purchase tickets from Munich Hbf to Geltendorf to cover your travel before 9 AM. These tickets are €7,20 pP, €18,80 for up to five. So, for two people leaving Munich at 8:52, transportation to and from the castles is €42,40, about $61).
Grayline, however, charges almost $162 to take two people to and from the castle, and you still have to pay for you castle tickets, which always includes a guided tour.
Radius charges less per person for the trip, but uses the train and bus.
When I was last there (Labor Day weekend), I arrived at the ticket kiosk at 11:30 and they were booking the 12:40 tour. (It takes a half hour or more to walk up to Neuschwanstein.) You can call ahead up to the day before and reserve a tour time for €1,80 pP.