Simultaneous spatiotemporal confinement of energetic electron pulses to femtosecond and nanometer scales is a topic of great interest in the scientific community, given the potential impact of such developments across a wide spectrum of scientific and industrial applications. For example, in ultrafast electron scattering, nanoscale probes would enable accurate maps of structural dynamics in materials with nanoscale heterogeneity, thereby leading to an understanding of the role of boundaries and defects on macroscopic properties. On the other hand, advances in this field are mostly limited by the brightness and size of the electron source. We present the design, fabrication, and optical characterization of bullseye plasmonic lenses for next-generation ultrafast electron sources. Using electromagnetic simulations, we examine how the interplay between light-plasmon coupling, plasmon propagation, dispersion, and resonance governs the properties of the photoemitted electron pulse. We also illustrate how the pulse duration and strength can be tuned by geometric design and predict that sub-10-fs pulses with nanoscale diameter can be achieved. We then fabricate lenses in gold films and characterize their plasmonic properties using cathodoluminescence spectromicroscopy, demonstrating suitable plasmonic behavior for ultrafast nanoscale photoemission.