Comparison of C-Cl bond length in CH3Cl and CF3Cl
The paragraph you cite does not define Bent's rule (see What is Bent's rule?, Utility of Bent's Rule - What can Bent's rule explain that other qualitative considerations cannot?). 

If you compare $\ce{H3CCl}$ and $\ce{F3CCl}$, then the $\ce{C-H}$ bond has less carbon-p character than an idealised sp³ orbital, while the $\ce{C-F}$ bond will have more carbon-p character than the idealised sp³ orbital. This in turn means that in $\ce{H3CCl}$ the $\ce{C-Cl}$ bond will have more carbon-p character as an idealised sp³ orbital and is therefore longer, while in $\ce{F3CCl}$ the $\ce{C-Cl}$ bond will have less carbon-p character and will therefore be shorter. 

Note of caution: I have read many questions about the concepts introduced in J. D. Lee's Concise Inorganic Chemistry; many of which revolve around outdated theories. I do not have a copy of that book, but from what I have experienced so far, I do not think it is a good book. Alas, in this instance it appears to be correct though.