Okay...
The JR East railpass will get you there on either train line.
Your real problem is the bus. You should be able to walk up to someone (preferably in a uniform) in the train station and ask for the location of the bus to Takaragawa Onsen (takaragawa onsen no bassu wa dochira desu ka?).
Osenkaku Ryokan gives this info about bus lines (of course, to their onsen, but...:It is about a 2 hour and 15 minute ride from JR Ueno train station in Tokyo to JR Minakami train station.
From JR Minakami train station on the Joetsu Rail Line, go out the exit and turn right. There are several bus stops outside the station. Get on the bus bound for "Takaragawa Onsen" and it leaves JR Minakami train station at 14:25 and 16:25. These times change from season to season so please see your confirmation e-mail for more accurate times. When you get on the bus, tell the driver you wish to go to Takaragawa Onsen (they speak a little English). It is a short walk from the Takaragawa Onsen Bus Stop to Osenkaku.
If you cannot make these 2 buses there is another route. Take the Kanetsu Kotsu Bus (bound for Yunokoya) at JR Minakami train station, and this bus will take you to Takaragawa Iriguchi Bus Stop. It is about a 30 minute bus ride. At Takaragawa Iriguchi Bus Stop take the yellow shuttle bus to Takaragawa Onsen (only a 3 minute bus ride). Check-in time at Osenkaku is after 14:00 so please take the Kanetsu Kotsu Bus leaving from JR Minakami train station at one of the following times: 13:41, 15:47, and 16:45. These times also change from season to season so please see your confirmation e-mails for more accurate times.
There's an article from Metropolis that also gives some instructions -
http://metropolis.co.jp/tokyo/412/japantravel.asp
Since a lot of the sites say "There is a bus that will take you directly to Takaragawa Onsen," there's a chance that there will be a sign in English. Additionally, since the various ryokan up there are at least advertising to non-Japanese, it's also possible that they'll have their own signs up to explain.
You can also print out a copy of this map -
http://japaneseguesthouses.com/db/gu...bunzan_map.gif - and you could always point to the place you want to go and show it to someone.
(Clearly, I'm supposed to be studying for an exam tomorrow.)