Does Bent's Rule only apply to molecules where there is hybridisation?
Bent's rule is not as much a rule as it is an observation. It was first applied in the context of valence bond theory and therefore used for hybrid orbitals only. At the initial stages, VBT only used s, sp, sp2, sp3, and p type orbitals. Bent proposed to allow also anything in between aiming at more flexibility for the wave function and therefore better accuracy of the description. As such it is only a tool for an already approximate view on bonding.

Most importantly, and in any and all general cases, the hybridisation state of the orbitals is determined by the molecular structure. For any case in which hybrid orbitals are used, there is also a true solution which does not use them.

Though Bent's rule has some predictive character for anything that is close to hybrid orbitals, it is basically just a shorthand for a much deeper rooted phenomenon. 

However, Bent's rule is not useful in any case where there is a low s-p mixing, i.e. anything below period 2 is a stretch.