Typically, I'll ship ammo (UPS) as soon as possible to the MD provided address or range (email them for address if not clearly stated). That way I can track the ammo and confirm it has been delivered. If any issues come along I still have plenty of time to either ship again or carry with me via luggage.
Regarding hand-off to UPS, you can either do so at the UPS DC or with a UPS driver, not at the UPS stores.