  Qubits encoded in hyperfine states of trapped ions are ideal for quantum
computation given their long lifetimes and low sensitivity to magnetic fields,
yet they suffer from off-resonant scattering during detection often limiting
their measurement fidelity. In ${}^{171}$Yb$^{+}$ this is exacerbated by a low
fluorescence yield, which leads to a need for complex and expensive hardware -
a problematic bottleneck especially when scaling up the number of qubits. We
demonstrate a detection routine based on electron shelving to address this
issue in ${}^{171}$Yb$^{+}$ and achieve a 5.6$\times$ reduction in single-ion
detection error on an avalanche photodiode to $1.8(2)\times10^{-3}$ in a 100
$\mu$s detection period, and a 4.3$\times$ error reduction on an electron
multiplying CCD camera, with $7.7(2)\times10^{-3}$ error in 400 $\mu$s. We
further improve the characterization of a repump transition at 760 nm to enable
a more rapid reset of the auxiliary $^2$F$_{7/2}$ states populated after
shelving. Finally, we examine the detection fidelity limit using the long-lived
$^2$F$_{7/2}$ state, achieving a further 300$\times$ and 12$\times$ reduction
in error to $6(7)\times10^{-6}$ and $6.3(3)\times10^{-4}$ in 1 ms on the
respective detectors. While shelving-rate limited in our setup, we suggest
various techniques to realize this detection method at speeds compatible with
quantum information processing, providing a pathway to ultra-high fidelity
detection in ${}^{171}$Yb$^{+}$.
