Ozegahara marshland from Utsunomiya

I'm planning to go Ozegahara marshland for a day trip on mid of Oct weekend. But i'll be staying in Utsunomiya.

1. What is the best way to go Ozegahara marshland from Utsunomiya? (by train / bus / tour?)

2. Which trailhead is more convenient to access for me from Utsunomiya?

3. Could anyone send me bus timetable link for the access to the possible trailheads?

It sounds better to stay closer to Hatomachitoge trailhead, for example near Takasaki Station or Numata Station.
(Here the second "o" in "Hatomachitoge" is pronounced long.)
Even if you fully utilize Shinkansen, it seems to take about 4 and a half hours to get from Utsunomiya to Hatomachitoge.

- japan-guide.com: Oze National Park
http://www.japan-guide.com/e/e7440.html
: See "From Tokyo via Gunma Prefecture" under "Get There and Around" section in this article.

Expected required time to hike between Hatomachitoge trailhead and Yamanohana Visitor Center is
1h 00 min for hiking down from Hatomachitoge trailhead
and 1 h 30 min for hiking up back from Yamanohana VC.
https://www.oze-fnd.or.jp/db/route/route-en.php?id=56

Expected required time to hike on the course between Yamanohana Visitor Center and Ryugu Crossroad, which is the most popular course in Ozegahara marshland, is 1h 20 each on the way and on the way back.
https://www.oze-fnd.or.jp/db/route/route-en.php?id=57

So, with your time to have rests and a lunch taken into account, you had better plan to secure at least 6 hours for the route Hatomachitoge -- Yamanohana -- Ryugu.
However, in order to secure 6 hours for this route, you seem to have to leave Utsunomiya Station extraordinarily early before 05:00.

----The earliest connection to get from Numata to Hatomachitoge----

In a case where you stay near Numata Station,
you can take a bus departing at 07:20 for about 1 and a half hour to Tokura and catch a shuttle bus departing at 08:55,
in which case you can use about 7 hours for the route.

Numata Station bus stop {07:20}
| [Kan-etsu Kotsu Bus]
{08:43} Bus connection office in Tokura for Hatomachitoge shuttle buses;
Tokura bus stop {08:55}
| [Kan-etsu Kotsu Bus]
{09:30} Hatomachitoge bus stop.

----The earliest connection to get from Utsunomiya to Hatomachitoge----

Entrance gate for non-Shinkansen Line:
Utsunomiya Station {04:37}
| [Utsunomiya Line]
{05:53} Omiya Station
: Shinkansen transfer gate:
Omiya Station {06:34}
| [Shinkansen: TOKI 301]
{06:58} Takasaki Station
: Shinkansen transfer gate:
Takasaki Station {07:10}
| [Jo(')etsu Line]
{07:56} Numata Station: Exit gate;
Numata Station bus stop {08:02}
| [Kan-etsu Kotsu Bus]
{09:30} Bus connection office in Tokura for Hatomachitoge shuttle buses;
Tokura bus stop {09:40}
| [Kan-etsu Kotsu Bus]
{10:15} Hatomachitoge bus stop.

----The earliest connection after 06:00 to get from Utsunomiya to Hatomachitoge----
Entrance gate for Shinkansen:
Utsunomiya Station {06:26}
| [Shinkansen: NASUNO 254]
{06:54} Omiya Station {07:02}
| [Shinkansen: Max TANIGAWA 401]
{07:34} Takasaki Station
: Shinkansen transfer gate:
Takasaki Station {07:45}
| [Jo(')etsu Line]
{08:33} Numata Station: Exit gate;
Numata Station bus stop {08:40}
| [Kan-etsu Kotsu Bus]
{09:58} Bus connection office in Tokura for Hatomachitoge shuttle buses;
Tokura bus stop {10:20}
| [Kan-etsu Kotsu Bus]
{10:55} Hatomachitoge bus stop.

----The last connection to get from Hatomachitoge----
(During 13 October - 3 November 2015)
Hatomachitoge bus stop {16:30}
| [Kan-etsu Kotsu Bus]
{17:00} Tokura bus stop;
Bus connection office in Tokura {18:30}
| [Kan-etsu Kotsu Bus]
{19:52} Numata Station bus stop;
Numata Station {20:27}
| [Jo(')etsu Line]
{21:13} Takasaki Station
: Shinkansen transfer gate:
Takasaki Station {21:38}
| [Shinkansen: Max TOKI 348]
{22:02} Omiya Station {22:10}
| [Shinkansen: YAMABIKO 223]
{22:34} Utsunomiya Station.