Spoilers for up to Season two Episode 15 - "Tales of Ba Sing Se". Proper plumbing is quite important to Zuko. -------------------------------------------------------------------
Space in the lower ring was at a premium and you were lucky to find a room to rent let alone a room with a private bath; an unheard of luxury here. Your options, Zuko was disgusted to learn, were to go to one of many public baths or to avail yourself of an alley with a pot of warm water. It was a far cry from what had been available to him aboard his ship; let alone what he had grown up with.
He just didn't feel clean unless he had soaked in hot water; in private. But as he wasn't going to get privacy either way, he opted for the choice that offered the most hot water.
Every second day he and his uncle would trek four blocks to the neighborhood communal bath, pay too much for too little, and join the other men on their designated side of the establishment. There were strict rules against peeping over the partition wall, but when Zuko pointed out to his Uncle there seemed to be no means of policing the rules he was told there were unspoken traditions in a public bath house that he'd only learn through observation and experience.
The last time Uncle had said something about 'learning through observation and experience' in that tone of voice it had resulted in an evening spent in the company of a large-breasted girl, a considerable dent in his purse, and his first kiss. It had been nice but entirely too risky to try again!
Girls were nosy and asked too many questions for him to keep up with the lies he had to respond with and they made him feel funny and do stupid, risky things... like lighting the lamps around a fountain in a public place using fire bending, with who knows who watching. That had been stupid and he knew it was going to come around and bite him in the face; he'd never be so lucky as to get bitten on the ass.
Scrubbing down was the most embarrassing part of the bath house. He'd sit on a little stool, naked, with a pot of water at his feet and try to clean himself while ignoring young boys running around disrupting everyone, old men asking for help washing their backs, whispered invitations he barely understood from suspicious looking men, and Uncle singing while he washed.
Uncle was the most distracting because it was nearly impossible to pretend he didn't hear him and he often got the other men to sing along to popular songs. When they would reach the end of a song the other side of the partition wall would erupt in giggles, catcalls, and invitations to entertain later in the evening. Uncle always responded with the suggestion they could find him at the tea shop where he brewed the best tea in the city.
Uncle's infamy at the bath house reflected onto Zuko and spawned more embarrassment when ladies would stop by the tea shop to ask if he was as accomplished an 'entertainer' as his uncle. He didn't like the way they'd emphasize the word 'entertainer', like it had another meaning they were trying to allude to. He could have asked his Uncle what they meant by it but he felt it was best to keep this to himself; he wasn't sure he'd like the imagery his uncle's explanation would bring to mind.
The only redeeming aspect of the public bath was the hot soak pool. It could seat a dozen average men with ease, was deep enough to reach your neck if you hunkered down, and was hot enough to turn your skin red.
Zuko never rushed his scrub-down but he did make sure he was as efficient as possible so not a moment was wasted that could be spent soaking.
Sometimes he'd stay in there until he felt himself drifting off to sleep and in his half-dreaming state he'd feel he was back Home; but he never allowed himself the luxury of sinking into that fantasy. Even in his dreams he knew there was no longer a place for him in the Fire Nation; not unless he made one for himself.
Uncle said the idea of making a place of your own also applied to Ba Sing Se and to anywhere else a man might settle down. Zuko thought about his words in the quiet moments at the tea shop, walking through the market in the morning, at night with the noises of the community surrounding him, but he knew that even if he could abandon his ambitions Ba Sing Se was not the place for him; the place he made for himself would include a proper, private bath.