It is possible to visit Neuschwanstein Castle from Munich without using the services of a tour operator. The return fare for the 2 hour train journey to Fussen is 32 euros for an adult, if you wait until after 9am to leave. The bus from Fussen to Hohenschwangau is a few more euros and to avoid a 45 minute walk up the hill you will need to pay a few more euros again. However, unless you have reserved your timed-entry ticket to the castle online in advance, you may find you have made the entire journey for nothing. This is no joke - we saw plenty of people turned away, because although 60 tourists are shunted into the castle every 5 minutes, there are still many more people who want to visit than can be accommodated.
When we realised we had left it too late to reserve a castle ticket we decided to book a tour from Munich through La Vacanza Travel. The tour was actually delivered by a company called Radius, and specifically conducted by a Texan ex-teacher called Austin. This cost us 41 per person, not including entrance to the castle, which had to be paid for separately. The crucial point is that Radius had reserved the tickets so we were certain to get in. And it cost us almost exactly the same as doing it independently would have done.
So even if Austin had been a rubbish guide, I would still recommend this tour. But Austin was the very antithesis of a rubbish guide. He is a natural educator, an entertainer, a great enthusiast for Bavaria, very funny, very knowledgeable about history and very thoughtful in his analyses. I particularly liked the analogies he drew between historical figures and modern celebrities, such as Bill Clinton, Donald Trump and Michael Jackson, which helped us to understand how they were viewed in their time.
Within the castle walls we had to have a state tourist board guide, who was awful. But whenever Austin was with us, on the platform, on the train, on the bus, in the queue for the Marienbrucke where the classic castle photo is taken he was stuffing us full of knowledge. Thank you Austin, you made a day trip into a truly memorable experience.