There are basically two ways with Kanto Area Pass:
1) Ltd Exp Kusatsu to Naganohara Kusatsuguchi then bus (2 hr 30 min+25 min)
2) Hokuriku (ex Nagano) Shinkansen to Karuizawa then bus (1 hr +75 min)
Route 1) may or may not be short-cutted by taking Shinkansen between Tokyo and Takasaki, depending on schedules, which you can check yourself by using Hyperdia or Jorudan. Things depends on time of departure and whether you'd want to stopover on the way (Karuizawa is a popular resort town), so I think you should research on various possibilities.
Bus is not covered by JR East's Pass.Edited: 22 August 2015, 09:51