In a modest society, bathing is in private, but some cultures have people bathing together, whether coed or not. We typically mean using soap, but a Korean Bathhouse has people soaking in a variety of pools of varying water temperate, even saunas. These can also be coed or not. A culture clash on modesty is easily done for this, with value judgments being made.
How often do people bathe on average? This often reflects a society’s understanding of hygiene, with SF worlds tending toward better education. Our fantasy characters may get one bath a week, taking any reasonable chance to swim in the interim. And a bath it likely is, not a shower, due to technology. Rarity may promote the use of perfumes as deodorants, with higher society possibly overdoing it, though they likely have more frequent bathing, a fact that easily distinguishes them from commoners; better kept clothing does the same.
Parents bathe children, but at what age does this stop? When do kids go it alone? If self-reliance is important, this may be earlier. If a child is rare (due to something like overpopulation that means a couple only gets to have one), then perhaps the parents fawn over a child and bathe him until he’s older. Does one parent or both assume responsibility for this? A child may also join either parent in a bath, meaning the parent is bathing, too. We might also see a family bathe together, all genders. If hot bath water is a luxury, decide who enjoys it first and last. We can use this when a character who got it last as a child, for example, gets the rare chance to go first as an adult and thinks about this during the scene, thinking back to childhood. Even without the luxury of warm water, who gets to go first when bath water in a tub must be shared?
At what time of day do people bathe, morning or night? It’s seldom midday but could be, particularly in a culture with a midday siesta due to heat. Those who are apt to get dirty during the day will likely pick night to avoid getting their bed dirtier than necessary, so this may apply to blue collar workers more than princes, for example.