Hourly Private Ryokan in Hakone?

I will be travelling to Tokyo with my gf early December and we have hotel booked for every night in our trip. However, we would really like to experience the hot springs in Hakone! Due to the fact that we already have hotel accommodation in Tokyo, we cannot book a night in a ryokan with private bath.

Does anyone know if there are any ryokans or hot springs that have hourly or some sort of package that doesn't include a night stays, but has private bath and possibly a dinner meal included?

I have done EXTENSIVE research and there doesn't seem to be one, but I'm sure I've seen travel shows where this is possible.

Please advise! =)

I think there are a few public bath houses and possibly some ryokan in the Hakone area that open their private baths to visitors. The only one that immediately comes to my mind is the Rakuyujurin Shizenkan, which gets introduced here:
http://www.japan-guide.com/e/e5209.html

The Rakuyujurin Shizenkan has some private baths, and advace reservation is recommended.