First of all, both those sentences are wrong.
It should be "Bjørnen sover ikke om natten" and "Brørnen sover ikke i natt".
The first one means "The bear doesn't sleep in the nighttime", while the second one means "The bear doesn't sleep tonight".
"Om" can mean both "about" and "if". It can also be used as "in" when it comes to time of the day. E.g. "om morgenen", "om kvelden", "om dagen", "om natten".