From Tokyo to Kusatsu Onsen

I learn from this web that I can take shinkansen to Karuizawa then take Seibu Bus or Kusakaru Kotsu to Kusatsu onsen but I can't find the email or website of these buses to check if they still operate and their current timetables because some don't run anymore after 2 covid years. I'm afraid of arriving Karuizawa but can't find bus to the town and return on time. Please help me how to contact them and if this shinkansen is covered by JRP all Japan? I'm not Japanese so I can only email in English, can't call because not understand Japanese. Thanks much!

This seems up-to-date:
http://www.kkkg.co.jp/bus/timetable/en-timetable.pdf

Seibu Bus operates on weekends and holidays only.
Karuizawa �� Kusatsu Onsen, 09:30 �� 11:10;
Kusatsu Onsen �� Karuizawa, 12:05 �� 13:36
For ref:
https://www.seibubus.co.jp/docs/rosen/karuizawa/eki.pdf
https://www.seibubus.co.jp/docs/rosen/karuizawa/onsen.pdf

JR Pass covers the Shinkansen trip to Karuizawa, but not the bus from Karuizawa to Kusatsu Onsen.
If you want JR Pass to cover the entire trip, you can board the special express train "Kusatsu" from Ueno Station (in Tokyo) to Naganohara-Kusatsuguchi Station directly (no transfer), then board the JR Bus to Kusatsu Onsen (covered by the JR Pass).

I went there in early December.
https://www.japan-guide.com/e/e7403.html

Thank you all for your replies. So you had visited there in the early December 22. (Actually I don't understand much the table :( :P) So which way you choose, Seibu or Kusakaru bus? Should I buy the ticket in advance or easily to buy it at bus stop after arriving Karuizawa? Is it easy to buy ticket on the way from Onsen back to Karuizawa to take shinkansen to Tokyo? Thanks again

I went by the second route (from Ueno, special express train), so I do not know the situation in Karuizawa. But once in Kusatsu Onsen, there is a bus terminal building where all 3 bus companies use for arrival and departure. https://goo.gl/maps/6GgHx4HaYzeHo7AC7

I did not have to make any bus reservation when I went. Unless you go during a major holiday, getting a ticket should be no problem.

So u chose the express train from Ueno, which is also covered by JRP, right? I myself booked the express bus from Shibuya to Onsen without transfer but I am considering to cancel it because I want to take use of JRP. One more question, please: what time did u start at Ueno station and arrive Onsen? Do u think it convenient? And what time did u start back from Onsen and arrive Tokyo? Thanks

My itinerary was a little different from yours, but it was 100% covered by the JR Pass.

From Ueno, I took the first express train of the day "Kusatsu No.1" (weekday, there is an earlier train on weekends and holidays), departing at 10:00am and arriving Naganohara-Kusatsuguchi at 12:18pm. There were 5 full size buses waiting for all passengers to go to Kusatsu Onsen, so there is no need to rush to catch the bus. They are JR buses, so the ride is free for JRP holders and the ride was about 25 minutes.

I did not return to Tokyo, so this part of my trip may not be applicable to you. I went to Takasaki on a regular train (non-express) then boarded the Shinkansen to Nagano. Going to Takasaki for a trip to Nagano may seem like backtracking too much, but I needed to be in Nagano as early as possible. I took the 6:20am bus from Kusatsu Onsen to board the 7:05am regular train, arriving Takasaki at 8:30am, then onto Nagano.

If returning to Tokyo (Ueno), the earliest express train during weekdays is "Kusatsu No.2". For that you can board the bus that departs Kusatsu Onsen at 12:00 noon, then board Kusatsu No.2 that departs Naganohara-Kusatsuguchi at 1:07pm, arriving Ueno at 3:26pm.

Check this site for the full train schedules (click the English language option):
https://www.kusatsu-onsen.ne.jp/access/train01.php

When you visit kusatsu onsen ,I strongly recommend you to buy JR East gunma 1 Day Local pass =2370 yen

Tokyu bus offer round trip for 7830 yen karuizawa kusatsu onsen excursion ticket from shibuya Tokyo