How to get rid of brown dust in Gucci bag?

I have just gotten a vintage Gucci bag ┬áin the mail today. When I opened it brown dust was inside it. It is probably the fabric remains (suede, or leather?) crumbling inside, since it’s old. How can I get rid of it? It is getting all my things dusty! I have tried wiping it out with my hand, which doesn’t work out all that great. Then I tried blowing inside the bag which made the crumblies come out much more effectively. What should I try now?