Transport from Tokyo to Kusatsu Onsen

I'm planning to go from Tokyo to Kusatsu-Onsen on a weekday in Mid-Jun/2018.
I plan to buy the JR East Pass (Nagano, Niigata Area).
I found out that there are 2 transportation option to go from Tokyo to Kusatsu-Onsen
Option 1 : Tokyo -(JR Shinkansen)- Karuizawa -(草軽bus) - Kusatsu Onsen
Option 2 : Ueno - (JR吾妻線) - Takasaki (via Naganohara Kusatsuguchi) -(JR Bus) - Kusatsu onsen

My question :
1. Which option is cheaper (less money pay for transport excluded from JR East pass) ?
and how much extra need to pay (aside from JR pass)
2. Which option is faster?

Please advise. Thank you.

For Option 2, that description is not accurate.

The JR 吾妻線 [Agatsuma Line] is beyond Shibukawa Station.

Some Local trains
which go on the Joetsu Line from Takasaki Station
continue beyond Shibukawa onto the Agatsuma Line,
heading to Naganoharakusatsuguchi, Manza-Kazawaguchi
or this line's terminus Ōmae Station.

Also,
you can travel by Shinkansen
from Tokyo Station to Takasaki Station.

Probably the simplest option is
: Shinjuku (bus terminal in Busta Shinjuku)
or Tokyo Station (Yaesu South Exit JR Bus Terminal)
-(JR Bus Kanto: Expressway bus)-
Kusatsu Onsen.
This option is relatively slow,
and the bus line is not covered by any JR pass.
The one-way bus fare is around 3000 yen.
http://time.jrbuskanto.co.jp.e.wn.hp.transer.com/bk03010.html
http://www.jrbuskanto.co.jp.e.wn.hp.transer.com/bus_stop/shinjuku_bast...

Option 2
: Ueno -(JR Takasaki Line)- Takasaki
-(JR Joetsu Line (until Shibukawa) + JR Agatsuma Line)-
Naganoharakusatsuguchi
-(JR Bus Kanto)- Kusatsu Onsen.

Option 3
: Tokyo or Ueno -(JR Shinkansen)- Takasaki
-(JR Joetsu Line (until Shibukawa) + JR Agatsuma Line)-
Naganoharakusatsuguchi
-(JR Bus Kanto)- Kusatsu Onsen.

Trains | buses for Option 1, 2 or 3 are not very frequently available.
When you make good connections,
Option 1 | Option 3 takes about 3 hours.
Option 2 highly likely takes much more time than Options 1 and 2.

Your additional cost is estimated
at 2200 yen per way for Option 1
and at 700 yen per way for Option 2 | Option 3.

I plan to buy the JR East Pass (Nagano, Niigata Area)

One merit of choosing this pass is
that it's a flexible pass which can be used on any 5 days within 14 days.
https://www.jreast.co.jp/e/eastpass_n/index.html

On the condition
that you make this Kusatsu Onsen trip within 3 consecutive days,
the JR TOKYO Wide Pass is enough.
https://www.jreast.co.jp/e/tokyowidepass/

The both passes cover
the Shinkansen section Tokyo -- Ueno -- Takasaki -- Karuizawa
and the Agatsuma Line.

These two passes do not cover
the JR Bus Kanto lines or the Kusakaru Kotsu bus line.

[Option 1]

Additional cost
: 2200 yen per way for the bus ride.

Tokyo Sta., 06:52,
　　ASAMA 601,
　　08:09, Karuizawa Sta.,
　　08:30, Bus, 09:53.
Tokyo Sta., 07:24,
　　ASAMA 603,
　　08:43, Karuizawa Sta.,
　　09:10, Bus, 10:26.
Tokyo Sta., 08:44,
　　HAKUTAKA 555,
　　09:49, Karuizawa Sta.,
　　10:10, Bus, 11:33.

Note
: The next bus departure is scheduled to be at 11:50.
: The buses depart at Bus Stop No. 2
in front of Karuizawa Station's North Exit.

- Kusakaru Kotsu bus timetables
http://www.kkkg.co.jp/bus/timetable/180421karuizawa_kusatsu.pdf

[Option 3]

Additional cost
: 700 yen per way for the bus ride.

Tokyo Sta., 06:08,
　　TOKI 301,
　　06:58, Takasaki Sta., 07:26,
　　Local,
　　08:49, Naganoharakusatsuguchi Sta.,
　　08:54, Bus, 09:22.
Tokyo Sta., 07:52,
　　HAKUTAKA 553,
　　08:42, Takasaki Sta., 08:53,
　　Local (for Ōmae),
　　10:19, Naganoharakusatsuguchi Sta.,
　　10:26, Bus, 10:54.
Tokyo Sta., 09:28,
　　TOKI 313,
　　10:25, Takasaki Sta., 10:44,
　　Local (for Manza-Kazawaguchi),
　　12:04, Naganoharakusatsuguchi Sta.,
　　12:11, Bus, 12:36.