Some flowers you do not have to collect as soon as they are ripe. They will continue to stay on the plant for a little while but I would always try to collect before heavy winds move in. I have waited sometimes a week or so before collecting on a plant that I knew was ready. It all varies on the seed head itself. Your plant strikes me as that plant you don't have to be sitting right on top of it when the seeds mature. Though if you wanted yes you could bag the seed head with something that was a breathable mesh like bag. I wouldn't recommend putting a plastic bag on it, though that is just me.

Plants with pods are different. Once the seeds are ripe the pod opens and it will release the seed. Therefore bags are a great idea for plants with pods, especially tiny half penny size pods.