We report on a survey for Hα bow shock emission around nearby γ-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 Hα structures around two additional γ-ray pulsars, PSR J2030+4415 and PSR J1509-5850. These are the first known examples of Hα 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)x1045/(f_ H I_sin i) g.cm2. We also derive a distance d ~ 0.72 kpc for the γ-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 φWNM∼ 0.3 there should be a total of approximately nine Hα bow shocks in our LAT-targeted survey; given that seven such objects are now known, a much larger φWNM seems problematic.