[utsu]

Fujikuro is right. There are buses.

Buy your ticket downstairs in the arrival hall at the Keisei counter. Then proceed to the bus stop. At Terminal Two it's bus stop number 10, at terminal One - bus stop number 8.

Three hours is a very optimistic estimate, count on 4 to be safe.

Be sure to keep your ticket stub after boarding, you'll need it in Utsunomiya to claim your luggage. One suitcase will go into the luggage hold, if you have more, you'll have to drag it to your seat. Even if the bus is almost empty, the staff will not put 2 suitcases from the same passenger into the hold.