Did you mean Asaya Hotel in Tochigi, Kinugawa? (I could not find Asaya Hotel in Gunma Prefecture)
I think the only way to get to Tobu World Square by public transportation is by train, getting on Tobu-Kinugawa Line from Kinugawa Koen Station to Kinugawa Onsen Station and then walk for about 20 minutes. The cost is only ¥150.
There seems to be a bus from Kinugawa Onsen Station to Tobu World Square, so you can also take a but instead of walking. It takes only 5 minutes by bus, and the bus seems to come every 20 minutes from 9:00 AM to approximately 3:45 PM (timetable differs in summer and in winter)