I know there are hot spring rooms with no bed or hotel amenities-- just the semi-outdoor pool/tub and maybe some chairs. But it’s been many years since I’ve been to one. Can anyone recommend a place?
I just love how your english has evolved. Welcome to the club my friend!
For the OP . Have you considered wild hotsprings? Taiwan has thousands and are extremely private/romantic! Way more than could likely be found from a company.
There are a lot of places which offer hotspring-only rooms.
Probably the biggest/most well-known in Beitou are: Chuantang 川燙 or Huangchi 皇池.
Both have private rooms as well as the public spaces:
If you don’t need to be in/near Taipei, there are loads of hotspring places in Wulai or Jiaoxi which have these kinds of private hot spring rooms (and are more pleasant to my mind, though maybe that’s mainly because the water is from a different source and doesn’t smell of sulphur/bad eggs).
Wulai, there are many choices from nice to not so nice basic rooms (ask prices, can be sometimes discounted). If in South, Taitung south has many nice options.
There is not really a clear separation between hotel hot springs and non-hotel hot springs.
Hotel Hot Springs may also have hot spring rooms without beds.
Hot springs for daytime short time use may call themselves a hotel but may in fact not be a hotel and only open for short visits and may have rooms with beds and without beds.
Hot Springs may have rooms with beds and without beds or maybe a couch or some sitting surface of some sort.
There really so many variations some may be for short-term use in the daytime and overnight use at night or only get overnight use like a hotel during weekend and have rooms of either type.
If looking for a private hot spring room without a bed then look at all options and ask for that specific type.
You need a room with bed, hot spring tub, steam room/sauna, 7-head shower and spend the whole afternoon shower-soak-rest-steam-rest-soak-shower … , than enjoy a good dinner.