Magnetic multilayers are a promising platform for storage and logic devices based on skyrmion spin textures, due to the large materials phase space for tuning properties. Epitaxial superlattice structures of [Pt/Co/Cu]n thin films were grown by molecular beam epitaxy at room temperature. Spin-polarized scanning tunneling microscopy (SP-STM) of these samples was used to probe the connection between surface structure and skyrmion morphology with nanoscale spatial resolution. Irregular-shaped skyrmion bubbles were observed, with effective diameters from 20 to 200 nm that are much larger than the nanoscale grain structure of the surface topography. Nucleation, annihilation, and motion of skyrmion bubbles could be driven using the stray field of the ferromagnetic tip in repeated imaging, and spin-polarized current/voltage pulses. Our detailed comparison of STM topography and differential conductance images shows that there are no surface defects or inhomogeneities at length scales that could account for the range in skyrmion bubble size or shape observed in the measurements.