  We study the concept of Carrollian spacetime starting from its underlying
fiber-bundle structure. The latter admits an Ehresmann connection, which
enables a natural separation of time and space, preserved by the subset of
Carrollian diffeomorphisms. These allow for the definition of Carrollian
tensors and the structure at hand provides the designated tools for describing
the geometry of null hypersurfaces embedded in Lorentzian manifolds. Using
these tools, we investigate the conformal isometries of general Carrollian
spacetimes and their relationship with the BMS group.
