The correct time to collect the seed is the Fall (Autumn) so about now seems right. For more advice check out the link ...

Here is a link that might be useful: Euonymus alatus

Thank you dog daze! I REALLY appreciate your help and have a great day!~Angie :)

The first stage of the burning bush seeds should look like little bombs/fish. These will split open to reveal a growing red spherical object. Wait until these inner seeds get quite large. When you pick them, you will find a little hard sphere/seed inside them. I do not know if this coating should be removed though....