OB stars powering stellar bowshock nebulae (SBNe) have been presumed to have large peculiar velocities. We measured peculiar velocities of SBN central stars to assess their kinematics relative to the general O-star population using Gaia EDR3 data for 267 SBN central stars and a sample of 455 Galactic O stars to derive projected velocities v 2D. For a subset of each sample, we obtained new optical spectroscopy to measure radial velocities and identify multiple-star systems. We find a minimum multiplicity fraction of 36% ± 6% among SBN central stars, consistent with >28% among runaway Galactic O stars. The large multiplicity fraction among runaways implicates very efficient dynamical ejection rather than binary-supernova origins. The median v 2D of SBN central stars is v 2D = 14.6 km s−1, larger than the median v 2D = 11.4 km s−1 for non-bowshock O stars. Central stars of SBNe have a runaway (v 2D > 25 km s−1) fraction of 24%, consistent with the % for control-sample O stars. Most (76%) SBNe central stars are not runaways. Our analysis of alignment (ΔPA) between the nebular morphological and v 2D kinematic position angles reveals two populations: a highly aligned (σ PA = 25°) population that includes stars with the largest v 2D (31% of the sample) and a random (nonaligned) population (69%). SBNe that lie within or near H ii regions comprise a larger fraction of this latter component than SBNe in isolated environments, implicating localized ISM flows as a factor shaping their orientations and morphologies. We outline a new conceptual approach to computing the solar local standard of rest motion, yielding [U ⊙, V ⊙, W ⊙] = [5.5, 7.5,4.5] km s−1.