Kusatsu Onsen from Nagano

Hi all

Currently planning a trip to Kusatsu Onsen in November. Our previous stop is the city of Nagano so I would like to ask the best option to get to Kusatsu Onsen from there...
Is getting a train to Karuizawa the optimal route, then getting a bus? (Not really sure if I can trust this bus info I have found for myself https://www.kkkg.co.jp/bus/timetable/en-timetable.pdf)

Also, after Kusatsu Onsen we are heading back to Tokyo, I've read about highway buses that connect Kusatsu directly to Shinjuku but I couldn't find much information about that (specially looking for timetables)... Is it worth/any advantages for taking that option instead of the route by train?

Thank you very much in advance, for your time and any information provided :)

Is getting a train to Karuizawa the optimal route, then getting a bus?

Yes, that is the best route.

(Not really sure if I can trust this bus info I have found for myself https://www.kkkg.co.jp/bus/timetable/en-timetable.pdf)

As of now, this is the up-to-date timetable.

Also, after Kusatsu Onsen we are heading back to Tokyo, I've read about highway buses that connect Kusatsu directly to Shinjuku but I couldn't find much information about that (specially looking for timetables)

This is the current timetable:
https://www.jrbuskanto.co.jp/wp-content/uploads/e6_1.pdf

The lower table is the one in the direction of Shinjuku:
草津温泉バスターミナル refers to Kusatsu
バ ス タ 新 宿 refers to Shinjuku

... Is it worth/any advantages for taking that option instead of the route by train?

It is a personal preference. I personally hate bus travel. Noisy, confining and prone to delays. I personally always opt for trains unless they are considerably slower or otherwise incovenient. The obvious advantage of the bus is the door-to-door transport (assuming that Shinjuku is where you wish to head).