The bailey is the open courtyard. You see the dummies all around?
However, it took awhile for him to appear in my game too. I'd enter the lab then go right back out. At first no one was around, but after I entered the lab people started appearing, and Paladin Gunny appeared as well.
Just keep entering/ wasting time and he'll eventually show up in the courtyard (aka Bailey). --- I'm just sayin'