We present results of $^{23}\mathrm{Na}$ and $^{19}\mathrm{F}$ nuclear magnetic resonance (NMR) measurements on ${\mathrm{NaCaCo}}_{2}{\mathrm{F}}_{7}$, a frustrated pyrochlore magnet with a Curie-Weiss temperature ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{CW}}\ensuremath{\approx}\ensuremath{-}140$ K and intrinsic bond disorder. Below 3.6 K both the $^{23}\mathrm{Na}$ and $^{19}\mathrm{F}$ spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80%) of the NMR signal intensity: This proves a broad quasistatic field distribution. The $^{19}\mathrm{F}$ spin-lattice relaxation rate ${}^{19}(1/{T}_{1}$) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the spin freezing to the presence of bond disorder. This is corroborated by large-scale Monte Carlo simulations of a classical bond-disordered XY model on the pyrochlore lattice. The low freezing temperature, together with the very short magnetic correlation length not captured by the simulations, suggests that quantum effects play a decisive role in ${\mathrm{NaCaCo}}_{2}{\mathrm{F}}_{7}$.