Founding: Year -55 — An unknown bartender, tired of rowdy hooligans causing fights in his bar, tricks them into leaving by sending them off on an adventure.
Beginning the LBB: Year 0 — Under request of Illiard, the guild setup the first meeting of the Low Bar Brawlers and set forth the initial steps to their adventure.
When a problem is determined by the Council, they set form a quest and delegate the Bartenders to send forth adventurers to complete this quest. The Bartenders typically engage in some crafty showmanship at their bars which serve as the genesis for the adventurer parties.
The Bartender's Guild is a clandesine organization that typically responds to political favors if they give them an advantage in furthering their quests. They don't outright manipulate politics but if an evil leader were coming into power they would set forth quests to stop him.
The Bartender's Guild has little to no economic influence. Some quests given involve looting dungeons and returning wealth into circulation. The guild also takes sponsors to resolve quests, such as in the case of Gond with Mortis Lux.
The Bartender's Guild has at its command leagues of powerful adventurers active and in the field. While they probably couldn't take on a full military invasion they could certainly setup a strong resistance movement.