Originally from the word Fog, which is the English pronunciation of Fag, Fog is a more polite way to call someone a Fag without sounding crude. No matter what a Brit says, it always comes out sounding much nicer.
The word Bog has been added because it gives the word a verbal twist, and it is added in more friendly social settings.
"Who doesthat Fog think he is doing stealing my seat!?"
"This room is getting a little Foggy"
"Whats up Fog Bog! How was your weekend?"