Answer: The answer to your question really depends on what kind of bulb you are growing. Many spring bulbs such as daffodils and crocus should be left in the ground year round where they will continue to bloom and will multiply -- if well sited and allowed to grow their foliage to renew the bulb's strength. The foliage needs to grow and then mature or turn brown and dry up naturally. If it is removed too soon, the bulb will lose strength and decline over time.
Many popular tulip varieties will decline from year to year and need to be replaced every year for best blooming performance. Rock garden or cottage tulips are an exception and will usually perennialize and increase over time if planted in a good location.
Summer bulbs such caladium or canna or dahlia(technically not bulbs but often considered that way) can be dug in the fall and saved for replanting the next spring. These should increase in size each year and actually improve over time if well grown. These are not winter hardy so they must be lifted and stored if you want to keep them.
I hope this answers your question.
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