North Dakota is frequently visited by Manitobans, but the vast majority of travel there is by private car or by charter bus. No regularly scheduled buses (or flights for that matter, you'd have to connect in MSP or ORD if you wanted to fly between FAR/GFK and YWG).
Whatever scheduled bus or shuttle service has been provided in recent years has been on a here-today, gone-tomorrow basis... I think the Northern Sparrow shuttle was the most recent, but their internet presence seems to have disappeared so I'm guessing the company is no longer around.
That said, Beaver Bus Lines does run 1 day shopping excursions to Grand Forks... the only practical option apart from driving may be to call Beaver, book a day trip and just throw the return ticket away.