I've never even seen a Mountain Ash but I've dried berries from lots of other trees and shrubs by just clipping twigs or branches and standing in a container with no water. Or lay them out on newspaper or racks to dry. When I try something unfamiliar to me, I try a few just barely ripe (red) and some ripe, as often one type will last longer dried or shrink/discolor less. It's mostly just trial and error for me. Some might even drop off the stem once dried when you work with them so it might be better to make your wreaths with the fresh berries and let them dry on the wreath. Just pick a few twigs and experiment.

This is just to maybe get you started...still hoping someone who really knows their berries ~smile~ will chime in. Good luck. josh