You can plant your hyacinth bulb out in the garden after the flowers are finished. Just cut off the flowering stem, and plant the bulb about 4in. deep with the leaves still above ground of course. Let the leaves grow and make a new bulb as long as they are green. A little fertilizer or bone mean will help when you plant it, but not absolutely necessary.
It may not bloom next spring, because it was "forced" to bloom early this year. But it will certainly bloom the year after and probably for years to come after that. They usually bloom in March or April up in your neck of the woods.