This is an Etruscan bed-frame. Roman bed-frames were pretty much the same. It would have had a mattress on top of it, stuffed with feathers or straw, and wool blankets. This frame is made of bronze, so it has lasted and we can see it. But most Etruscan and Roman beds would have been made of wood and strung with wool or linen string. (We still make lawn chairs in about the same way that the Romans made beds.)
Many people probably didn’t have mattresses. They slept right on the strings, or on straw mats laid on top of the strings. Cloth – because people had to spin and weave it by hand – was too expensive for most Roman people to use on bedsheets or mattress covers.
However, throughout human history, nearly everybody has slept with some sort of covering. People in ancient Rome slept with covers too. They generally had a wool blanket or a linen sheet. Some people used their outdoor cloak, or their veil, as a blanket at night.
And some people, especially people who were enslaved, had to sleep without a bed at all. They probably slept on straw mats right on the floor.
Learn by doing: try sleeping on a lawn chair laid flat, or in a hammock.
More about Roman houses
Ancient Rome (Eyewitness Books), by Simon James (2004).
Ancient Rome: A Guide to the Glory of Imperial Rome, by Jonathan Stroud (2000). A day as a time-travelling tourist in ancient Rome, for kids.
Houses, Villas, and Palaces in the Roman World, by Alexander McKay (1998).