We present ~2'' resolution interferometric maps of the 12CO J=2-1 emission in the PPN IRAS 19475+3119 obtained with OVRO. These data probe two distinct molecular components, namely, a slowly expanding shell and a fast bipolar outflow.We have used a spatiokinematic model of the 12CO J=2-1 emission to constrain the properties of these two components. The shell has inner and outer radii of Rin~6.5×1016 cm and Rout~2×1017 cm and expands at Vexp~11 km s-1. The 12CO J=2-1 line wing emission arises in a bipolar structure that emerges from two diametrically opposite holes in the slow shell. The bipolar outflow is aligned with one of the two lobe pairs of the quadrupolar optical nebula (at P.A.~80deg). Both the holes and the bipolar outflow are most likely the result of the interaction of fast, collimated post-AGB winds with the shell. The quadrupolar morphology of the optical nebula indicates two distinct bipolar post-AGB winds ejected in two different directions. The elongation of the optical counterpart of the shell (at P.A.~-45deg) and two similarly aligned CO clumps suggest that the slow shell has also been affected by the wind interaction. The expansion velocity in the bipolar outflow increases linearly with the distance from the nebula center and reaches Vexp=30 km s-1 (projected) at the tips of the lobes. This velocity gradient yields a relatively long kinematical age of ~1900 yr, assuming an outflow inclination of i=30deg with respect to the plane of the sky; this age is comparable with the post-AGB lifetime estimated from the shell expansion velocity and inner radius. We derive a mean kinetic temperature of ~14 K and a total mass of ~0.4 Msolar. The collimation and linear momentum (P~4×1038 g cm s-1) of the outflow are unlikely to result from radiation pressure on dust grains.