A Bawse is a human being who exudes confidence, turns heads, reaches goals, finds inner strenght, gets hurt efficiently and smiles genuinely- because they've fought through it all and made it out the other side. The double-handed praise was created for them.
In a bawse world there are no escalators, there are only stairs.
In the Grand Theft Auto universe, it's the official stock exchange. Parody/Equivalent of real-life NASDAQ. Oh I forgot. Of course it sounds like "ballsack" that's the point. The name derives from the Scottish slang it seems.