BP = Battle Points. Earned from attacking/raiding rivals (Yellow circle w/ crosshair points). Select the "RANKINGS" tab on the rivals list to find out where you stand.
XP = Experience points. Earned from doing missions and attacking/raiding (Yellow star points).
Don't confuse the two. Mission only players can be level 200 and still hold the rank of Private. But to get rank rewards, you'll have to do a lot of attacking/raiding.
IF you have 110K BP's, then you have the rank of Lieutenant and will find the Expert Attack Drone from the buy unit's screen in under the Ground tab...Just scroll right.