Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of $^{87}$Rb, between the $|rm{F} = 1, rm{m_F}=1 rangle$ and $|rm{F} = 2, rm{m_F}=0 rangle$ states. Despite the loss features being $lesssim0.1$ G wide, we require only 21 experimental runs to explore a magnetic field range >18 G, where $1~rm{G}=10^{-4}$ T. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G and two previously unobserved p-wave features near 5 G and 10 G. We further utilize the dispersive approach to directly characterize the two-body loss dynamics for each Feshbach resonance.
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