Iroh left Ba Sing Sei after his son died...it would take some time for news to travel back home in this world with its low technology, so he would be well away from it by the time that letter reached the Fire Nation capital...furthermore, he never had access to the city...that was the point. He was trying to crack it with a siege but failed. And why would she want to hide in a foreign city at war with her homeland?
Speaking of Iroh, it was weird and kinda scary to hear him make that joke about burning Ba Sing Sei to the ground...it seems out-of-character for him to make such a vicious jest, though that's appropriate, of course, as he was different back then.