  The discovery of gravitational waves (GW) by Advanced LIGO has ushered us
into an era of observational GW astrophysics. Compact binaries remain the
primary target sources for LIGO, of which neutron star-black hole (NSBH)
binaries form an important subset. GWs from NSBH sources carry signatures of
(a) the tidal distortion of the neutron star by its companion black hole during
inspiral, and (b) its potential tidal disruption near merger. In this paper, we
present a Bayesian study of the measurability of neutron star tidal
deformability $\Lambda_\mathrm{NS}\propto (R/M)^{5}$ using observation(s) of
inspiral-merger GW signals from disruptive NSBH coalescences, taking into
account the crucial effect of black hole spins. First, we find that if
non-tidal templates are used to estimate source parameters for an NSBH signal,
the bias introduced in the estimation of non-tidal physical parameters will
only be significant for loud signals with signal-to-noise ratios $> 30$. For
similarly loud signals, we also find that we can begin to put interesting
constraints on $\Lambda_\mathrm{NS}$ (factor of 1-2) with individual
observations. Next, we study how a population of realistic NSBH detections will
improve our measurement of neutron star tidal deformability. For astrophysical
populations of $disruptive$ NSBH mergers, we find 20-35 events to be sufficient
to constrain $\Lambda_\mathrm{NS}$ within $\pm 25-50\%$, depending on the
chosen equation of state. In this we also assume that LIGO will detect black
holes with masses within the astrophysical $mass$-$gap$. If the mass-gap
remains preserved in NSBHs detected by LIGO, we estimate that $25\%$
$additional$ detections will furnish comparable tidal measurement accuracy. In
both cases, we find that the loudest 5-10 events to provide most of the tidal
information, thereby facilitating targeted follow-ups of NSBHs in the upcoming
LIGO-Virgo runs.
