It can be difficult to tell if your potted tulip was forced into blooming by looking at it. The only way you to tell is to try and replant it to see if it blooms again. Wait for the bloom to start to wilt and then cut off only the flower stalks. Do not damage the foliage in any way because the bulb uses the foliage to store energy. Allow the foliage to yellow and die away on its own. Keep the potted tulip in a cool, dry place and then replant it. Tulips require cold weather to bloom, so plant your potted tulip in late September to give it a chance to grow back. If you do not see small stalks in spring, then the bulbs are dead.
The soil the tulips were potted in was given the right combination of nutrients to grow the first set of bulbs. As tulip bulbs being to wilt, they replenish the soil around them using their foliage to prepare to hibernate. Allow the bloom and foliage on your potted tulip to wilt down to a yellow color. Then remove the old bulbs and plant new ones in their place. Store the pot in a cool, dry place and water the soil to keep it moist. Do not remove the old foliage because it still helps prepare the soil for the new bulbs.
A potted tulip that has not been forced will bloom again during its next cycle. If you do not have a garden to replant your tulip in but would like to see it bloom again, then store it in an area between 31 degrees and 40 degrees Fahrenheit, according to the Longwood Gardens website. Water your plant to keep it moist and then add liquid fertilizer every 10 days to maintain soil nutrients. If the tulip was not forced, then it will bloom again next year.
It can require work and patience to cultivate a potted tulip to the point where it has a chance to grow back. The chances that you will be able to replant a potted tulip in your garden successfully are not very good, according to the Country Living website. If you would rather avoid the potential disappointment of not having your potted tulip bulbs bloom again, then you can discard the plant after the bloom has started wilting.