I just got done some OCONUS travel (Europe at large) while on BDCP. Filling out a leave chit is all thats necessary, as long as you don't plan on visiting suspicious countries.
It gets a little more complicated if you plan on flying Space A. Those closest thing to legit papers we can use is a authorization for travel for reservists, and then you pretty much have to charm your way onto base. Good times...
If you have a military ID, there is no charming involved. ??