Question
do both male and female bloom white flowers?

Answer
The Dogwood flower is a small flower cluster. The flower cluster is surrounded by 4 large showy bracts that are often mistaken as petals. The four white "petals" aren't petals at all, but rather bracts, which are modified leaves. The actual flowers are the tiny greenish-yellow objects in the center of the thing people usually call dogwood flowers, but which is actually a flowering head. When the early spring flowers seem to present themselves before the leaves come out, they are actually modified leaves.

The small flower clusters on the Flowering Dogwood are surrounded by 4 large, showy bracts that are often mistaken as petals. Each quarter-inch flower has four tightly curved petals, plus two stamens and a single pistil. Flowers that have dropped their petals is a sign they likely have been pollinated. Eventually, after all the white bracts and tiny petals have fallen, the remaining flower parts will wither and turn brown, giving rise to several fertilized ovaries, the bright green berries that turn scarlet as they ripen.

In short the dogwood "flower" is composed of both male and female parts.