The Bed Cover Monster was the sheets on Calvin's bed. It appeared as a monster in a single weekday strip and in a single Sunday strip. Calvin got out of bed, however, the sheets grabbed him and pulled them into its "mouth." This is analogous to Calvin trying to get out of bed, as his mother asked him in the fourth panel. In the Sunday strip, it had a much smaller role. it simply picked up Calvin, and literally flung him down the stairs.
It is unknown if the Bed Covers Monster was mad about when Calvin and Hobbes were trying to get rid of the bedbug Calvin imagined.