Daffodils (narcissus) are the heralds of spring, being among the first of the perennial bulbs to bloom shortly after the last frost. Hyacinths (hyacinthus) follow in mid-spring, and lilies (lilium) bloom in late spring and early summer. The bloom schedules effect when these different flowers can be safely transplanted without risk of shock to the plants.
According to Eileen Powell's "The Gardener's A-Z Guide to Growing Flowers from Seed to Bloom," daffodils should be transplanted in autumn. Daffodils need the cold winter to trigger their dormancy which is required before they will bloom in the spring. They must be in the ground in the fall before frosts begin because they flower so soon after the ground begins to warm in spring.
Bulbs that have been started indoors or in a greenhouse may also be transplanted in late autumn in the South, or at the end of summer or early fall in colder regions further north.
Hyacinths can also be transplanted in autumn. When their foliage has died back in fall, dig them up and transplant them before the first frost in your area.
Hyacinths will bloom sooner for people who live in the southern hardiness zones (seven and eight), so it is particularly important for residents of those zones to transplant their hyacinth plants as soon as they can in the fall in anticipation of the first frost. Residents of zones five and six can probably wait until after the leaves have been killed by the first light frost before transplanting assuming the ground isn't frozen.
Depending on species, some lily plants will bloom in late spring while others will not show their buds until autumn. Therefore, transplanting the lilies requires you to know what their blooming season is. In general, lilies do need the cold of winter to prepare them for the next year's blooming, so they need to be in the ground before it becomes hard from frost.
According to lilybulb.com, lilies should be dug up and transplanted during the cool fall months when the leaves of the plants have turned yellow. For fall-blooming lilies, you will need to wait until after the blooms have waned and foliage has died back to allow the bulb sufficient time to recuperate before lifting it. This should occur before frost sets in in your area; however in colder zones you will need to act quickly if an early frost occurs.