If I recall, this is a novel series, right?
As a literary device to tie various captains together to tell stories from various times, it works fine. As I recall (from the only one of these books I actually read...) The barkeep told Pike that he could only know where to find the place or what location in time it was. Sort of a bizarre Heizenburg scenario.
Seemed like the sort of thing Doctor Who might explain with a phrase like "timey-wimey."
If we want a more Star Trek explanation, I propose that there is an entity (perhaps the barkeep?) who is like the Nexus Ribbon in that he/it exists in various times and places at once; extra-dimensionally. Also, this entity is telepathic and when he's in the vicinity of a captain, he connects to the captain's mind and telepathically and simulates the bar in that captain's mind while providing a mental conduit for communication amongst the other captain's.
Why does this entity do this? Why just captains? Clearly it's his hobby.
Having only read the one book several years ago, that'd be my explanation, but maybe it was actually explained at some point that I'm not aware of...
--Alex