Can you dig up tulip bulbs as soon as they finish blooming, leaving the leaves attached to the bulb so you can plant annuals in the same bed without waiting for the tulip leaves to wither.
Digging Up Tulips
If you want the tulips to bloom next year, leave them for the leaves to die down naturally. Flowering is very energy intensive and the bulb needs those weeks to rebuild / nourish the bulb. If you dig them up now, you might as well throw them in the compost which is what some people do. Another strategy is to plant something in front of them to disguise, but not entirely shade, the tulip leaves.