We present narrowband (Hα and adjacent continuum) and broadband (B and V) optical images of the dwarf Wolf-Rayet galaxy Zw 0855+06 and its companion, together with high-resolution Hα spectroscopy of the main galaxy. We find a bridge of ~14.7 kpc (~65") in length and stellar nature connecting both galaxies, a feature that undoubtedly indicates their mutual interaction. We infer from the narrow width of the bridge that at least one of these two dwarf galaxies had a well-developed disk before the interaction. The light of the main galaxy (M_B=-17.82) is dominated by a young and massive ionizing population. There is ample reason to believe that a gravitational interaction with the companion caused the starburst. The companion (M_B=-15.84) does not show any evidence of ionized gas, and its population has a B-V color that suggests the presence of intermediate-age (~10^9 yr) stars. This case highlights the concept that bursts in H II dwarf galaxies may be caused by interactions with lower luminosity companions. We anticipate that ruling out interactions as the origin of bursts in dwarf galaxies will require deeper surveys than are currently available. We find a backward outflow with a velocity of about 47 km s^-1 in the southeast part (~880 pc from the center) of the main galaxy, suggesting the presence of dynamical effects on the interstellar gas arising from the mechanical action of the massive stars or the interaction process.