You can sell it any time you want. How you ship it is the question... I am sure there is a way, and someone here will know. Where are you located?
The bullets (I assume you mean unloaded bullets in a Barnes box... for reloading) you can ship or do what ever you want with (even list them on ebay I think).... the loaded ammo (factory or hand loads) there are rules about shipping it.
As far as i know...you can ship ammo (any kind) door to door no problem. . I know if you buy actual factory ammunition off of somewhere like cabelas it will be delivered to your doorstep with no signature needed.
There are special restrictions on ammunition shipping, special markings and whatnot, I am pretty sure an individual can ship it though.It also has to go Fedex or UPS. I would check with the carrier first, you might need to talk to a few people before you find someone who knows the rules.