I've been told it's a dogwood and I've also been told it's a flowering sweet almond? Which is it? Or is it something completely different?
I'd say you can prune after the bush has finished flowering. If there are any all-green shoots, be sure to remove them.
"Young plants require little formative pruning. When established, each year cut back flowered stems to strong, usually upright, shoots below the faded flowers. Cut out at the base one or two old stems, aiming to maintain a balance between mature and young wood, and remove or shorten overlong new growth that ruins the plant's shape. Yellow- and purple-leaved cultivars may be cut back harder; remove about three-quarters of the old wood entirely and shorten the remaining stems by three-quarters. Cut out any reverted shoots on variegated cultivars. To renovate, cut all stems to ground level. Thin the new shoots in midsummer" --Brickell/Joyce, Pruning & Training (1996, DK Publishing, New York)
Thank you everyone for the information. This helps me a lot. I don't deal too much with bushes, I'm more into perennials.