Red Osier is my primary arrow shaft material. I use it for ALL of my roving and small game arrows.
I cut shoots in winter, and have always peeled them within a day or two of cutting them. There is some checking on the ends while they dry, but not enough to ruin a shaft. I tried leaving the bark on the ends of the shoots, but didn't notice much of a difference. Recently I did one where I left all of the bark on until the shoot was fully seasoned. It turned out really well, so this is probably how I will do it in the future, but it's really a personal choice. All three methods work just fine.
I don't bundle the shafts right away. I lay them out and let them dry for a while. After a week or so (maybe longer if the bark is still on) I start hand straightening them. There is a window of opportunity during the drying where you can do most of the straightening, and the partially dry shafts will keep the shape you give them. After this initial straightening is done, then I bundle them and put them away to finish seasoning.
How long you let them season will depend on your environment and whether you peeled them or left the bark on. I collect a new batch of shoots every winter, which is also when I do most of my arrow making, so I typically make arrows out of my previous year's collection.
NorthernArcher