The helical shape of the human stomach pathogen Helicobacter pylori has been suggested to provide mechanical advantage for penetrating the viscous stomach mucus layer. Using single-cell tracking and quantitative morphology analysis, we document marked variation in cell body helical parameters and flagellum number among H. pylori strains leading to distinct and broad speed distributions in broth and viscous gastric mucin media. These distributions reflect both temporal variation in swimming speed and morphologic variation within the population. Isogenic mutants with straight-rod morphology showed 7-21% reduction in speed and a lower fraction of motile bacteria. Mutational perturbation of flagellum number revealed a 19% increase in speed with 4 versus 3 median flagellum number. Resistive force theory modeling incorporating variation of both cell shape and flagellum number predicts qualitative speed differences of 10-30% among strains. However, quantitative comparisons suggest resistive force theory underestimates the influence of cell body shape on speed for helical shaped bacteria.