The "fish bladder" you may be thinking of is actually isinglass, a substance derived from the swim bladders of certain fish, primarily sturgeon. Isinglass was historically used as a fining agent in beer, including Guinness.
However, Guinness stopped using isinglass in 2005. They now use a vegetarian fining agent derived from algae.
So, while the myth persists, Guinness has been vegan-friendly for over two decades.