We report on a survey for H{alpha} bow shock emission around nearby {gamma}-detected energetic pulsars. This survey adds three Balmer-dominated neutron star bow shocks to the six previously confirmed examples. In addition to the shock around Fermi pulsar PSR J1741-2054, we now report H{alpha} structures around two additional {gamma}-ray pulsars, PSR J2030+4415 and PSR J1509-5850. These are the first known examples of H{alpha} nebulae with pre-ionization halos. With new measurements, we show that a simple analytic model can account for the angular size and flux of the bow shocks' apices. The latter, in particular, provides a new pulsar probe and indicates large moments of inertia and smaller distances than previously assumed in several cases. In particular, we show that the re-measured PSR J0437-4715 shock flux implies I=(1.7+/-0.2)x10^45^/(f_H I_sin i)g cm^2^. We also derive a distance d~0.72 kpc for the {gamma}-ray only pulsar PSR J2030+4415 and revised distances for PSRs J1959+2048 (1.4 kpc) and J2555+6535 (~1 kpc), smaller than the conventional DM-estimated values. Finally, we report upper limits for 94 additional LAT pulsars. An estimate of the survey sensitivity indicates that for a warm neutral medium filling factor {phi}_WNM_~0.3 there should be a total of approximately nine H{alpha} bow shocks in our LAT-targeted survey; given that seven such objects are now known, a much larger {phi}_WNM_ seems problematic.