The private mixed hot springs
Private onsen ♨️ is often referred to as a luxury that only few travelers in Japan can afford. Overall, most thought areas to find thermal sources are north of Japan (Hokkaido), Honshu (Hakone near Mount Fuji 🗻), or Kyushu island in the south. There are undoubtedly others, but these are reknown for the quality of their natural hot springs.
Private onsen sometimes comes as an annex to the room of a high-priced ryokan or as modern 'onsen spa' for quite wealthy clients. I have not had the opportunity to try these, but something slightly more modest at an affordable cost: 2,000 Yen 💴 for one hour (that's about $25). Financially, it's a great opportunity because even with the onsen in a hotel 🏨 room, you probably won't dip all night long.
The building is called Hyotan and is located in Beppu, Kyushu, in a traditional neighborhood northeast from downtown. Specifically, it's a few hundred feet from Happy Neko, a minshuku in this area. Hyotan also offers classic public bathrooms, but this range of 9 private onsen (indoor or outdoor) will suit families, lovers or prudish westerners.
Upon entering the private onsen, you'll hang a sign to indicate that it is reserved. As a matter of fact, the door does not lock. I guess this is related to water temperature, extremely hot (close to 50°C) which may cause some faintness. Rest assured, if the natural spring 🌸 fills your bath with its own temperature, it's possible to add cold water to adjust and avoid burning. At the end of the session, it's advisable not to rewash yourself because Beppu hotspring water has beneficial properties for skin.
The private onsen experience is very charming. There's a vestibule at the entrance where you can deposit clothes and it contains some cosmetics which your lady can use before going back out. In the onsen itself, there are obviously open showers to wash before entering the bath. The place is very traditional, with stone and a few plants, and everything is extremely clean. Aside from the large main onsen bath, there's also a small ice bath and a sauna.
Depending on your resistance to heat, one hour may be more than enough to enjoy the onsen experience in these conditions and, whatever your reasons, I can only encourage you to seek private sources.