Hi, zuzanaare you going Beitou alone or with some other people? Because this will be a critical issue to choose a hot spring. Yeah sadly, most of them are run by hotels with many bathrooms and the cost varies. It's not like what you see in the Japanese movie, bathing in a wild pool surrounded by snow, trees, and wild monkeys. But there are still hot springs like these in Taiwan.
for hot springs, there're many types provided with different pricing.
I am not sure what kinds of scene you wish to take, but I can tell you there're like:
a. just an interior bathroom with a bathtub. (some are wooden, while others are not), usually only for one or two person with private a room, with or without window. Most love couples and newly wed would choose this type.
b. larger bathtub with 3,4, 5 or even more. For family or party.
c. open arena like, Roman bathhouse.
d. bathhouse without ceiling so that you can see the the view of the mountains and mist.
Most of the public bathhouse are gendered specific. Some are mixed-gendered. Most of the bathhouses permit you to be naked. Some of them would request you to be dressed in swimsuit. Some are open even for 24hrs.
Sunya says she would like to be there on Sunday. But we are not yet sure if we are going by MRT or by some other means.