Bedtime was the time one was supposed to go to bed and sleep.
For children, bedtime often came with a bedtime story and being tucked in.
In 2152, Doctor Phlox noted that he had many animals to feed before bedtime, suggesting Hoshi Sato (leave sickbay and) get a good night's sleep. (ENT: "Vanishing Point")
In 2370, when asking questions about her mother Anetra, Taya was told that it was past her bedtime. (DS9: "Shadowplay")
In 2373, a worn out Quark decided it was his bedtime when Jadzia Dax suggested Worf wouldn't be able to help him if his body was too tired to fight for Grilka. (DS9: "Looking for par'Mach in All the Wrong Places")
Later, after a long day on Risa, Jadzia told Worf it was past her bedtime. (DS9: "Let He Who Is Without Sin...")
In 2374, Neelix offered to visit Naomi Wildman near her bedtime after hearing from her mother Samantha Wildman that the girl had been asking for him. (VOY: "Mortal Coil")
Twice while playing The Adventures of Flotter holoprogram with Naomi in 2375, Neelix had to tell her it was her bedtime. (VOY: "Once Upon a Time")
Later that year, Artim noted that Data, who had never been a child, had never had to experience such limitations as bedtimes, among other things. The android replied that he would gladly accept such limitations if he could have had a childhood. (Star Trek: Insurrection)
Also that year, after taking Naomi out on a ride in the Delta Flyer with Seven of Nine, Tom Paris offered to tell Samantha why her daughter was two hours late for bedtime if she started the survey report, to which Seven agreed. (VOY: "Bliss")
In 2381, Captain Carol Freeman enforced crew bedtimes on the USS Cerritos while reporter Victoria Nuzé was onboard. (LD: "Trusted Sources")