You don't tell us what kind of bush, Mags, but have a go. Anytime from now-ish til end of August is worth a try. We don't know if it's a flowering bush, but if it is pull off some non-flowering shoots 2 - 6 inches long, take off the lower leaves and arrange the shoots around the edge of a pot full of moist compost. Pop a clear plastic bag over the top of the pot, enclosing the cuttings, and keep it in place with a rubber band around the pot. Put on a light but not sunny windowsill and hope for the best. If you see new leaves appearing it's worth having a look to see if there are roots as well.

If you can only find flowering shoots (quite normal on Fuchsias, for example) pinch out all the flowers and buds as you want the cutting's energy to go into making roots, not flowers.