Single metal nanoparticles are attractive biomolecular sensors. Binding of analyte to a functional particle results in a plasmon shift that can be conveniently monitored in a far-field optical microscope. Heterogeneities in spectral properties of individual particles in an ensemble affect the reliability of a single-particle plasmon sensor, especially when plasmon shifts are monitored in real-time using a fixed irradiation wavelength. We compare the spectral heterogeneity of different plasmon sensor geometries (gold nanospheres, nanorods, and bipyramids) and correlate this to their size and aspect-ratio dispersion. We show that gold bipyramids exhibit a strongly reduced heterogeneity in aspect ratio and plasmon wavelength compared to commonly used gold nanorods. We show that this translates into a significantly improved homogeneity of the response to molecular binding without compromising single-molecule sensitivity.