The Bulk is an extra-dimensional region beyond the four dimensions - three spatial dimensions and one temporal dimension - of our universe. In the film, it is shown as the region inside a wormhole. As Romilly explained to Cooper in simplified terms, if space-time were represented in two dimensions as a flat piece of paper, a wormhole that would connect two points in this 2D space-time would be a dimension higher or in 3D as a Sphere. Applying this logic, the Bulk is essentially a dimension higher than our three-dimensional space.
The Bulk beings of the film reside within this dimension and have mastered the ability to manipulate gravity and space-time. They used this ability to create the wormhole that serves as the space-time bridge that humanity uses to scout for habitable planets beyond their solar system.