To get to Hōshi Onsen, take the bus from Jōmō Kōgen Station to Sarugakyō Onsen (¥880, 30 minutes) and change for the less frequent bus to Hōshi Onsen (¥600, 20 minutes).
If you're arriving by tokkyū train on the Jōetsu line, get off at Gokan Station (two stops before Minakami), then get the bus to Sarugakyō (¥1100, 40 minutes), where you should change to the bus for Hōshi Onsen (¥600, 15 minutes).
Buses depart regularly from both Jōmō Kōgen Station (¥3900) and Minakami Station (¥2900) for Takaragawa Onsen.
Timetables can be found at http://global.kan-etsu.net/en/minakami/yunokoya.html.
If you don't mind driving winding mountain roads, renting a car from Jōmō Kōgen Station (or Takasaki) is by far the best way to experience the area, giving you freedom to explore the divine onsen, the town of Minakami and the ropeway.
See the friendly staff at Toyota Rent-a-Lease, directly opposite Jōmō Kōgen Station.