private bath at Dogo Onsen?

We are planning to visit Matsuyama and would like to visit the famous Dogo Onsen. We would prefer to bath privately and I know some onsen offer ''family baths'' or short private bookings. Is this type of private bathing available at Dogo Onsen? Many sources on the Onsen discuss different levels of service but don't detail what the higher levels are. Thank you!

Several ryokan in Dogo Onsen should have private baths that can be used by staying guests. But I could not find any public baths that can be visited on a daytrip.

See, for example, the following list of ryokan:
http://www.japaneseguesthouses.com/db/dogo/