HR 3126 is an M2 II giant surrounded by the bipolar reflection nebula IC2220. A sensitive R-band image obtained with the ESO 3.6 m telescope shows that the nebula has a size of at least 10', corresponding to a linear size of about 1 pc, and is extended in the east-west direction. CO(1-0), CO(2-1), and 13CO(1-0) maps obtained with the Swedish-ESO Submillimetre Telescope (SEST) show line profiles that can be interpreted as an asymmetric east-west bipolar outflow in the inner 3' of the optical nebula. Due to the unusually large angular extent of the nebula it is well resolved even in single dish observations. We have modelled the outflow as a hollow shell, expanding radially with a velocity proportional to the distance from the star. Such a shell can be created by a high velocity wind expanding into a previously ejected asymmetric low-velocity wind. The mass loss event traced by the CO emission started quite abruptly about 8000 years ago. The CO emission also traces an equatorial density enhancement, possibly a fragmented disk, perpendicular to the outflow. The CO excitation temperature in the outflow is quite low, about 3.8 K, as determined from the (1-0)/(2-1) line intensity ratios. The total mass of the gas in the nebula is larger than 0.5 M_odot. We also searched for SiO and OH masers, as well as emission from SiO (v = 0, J = 2-1), HCN (1-0), HCO^+(1-0), and CS(2-1), but without detections. The evolutionary stage of the central star is not clear. It is unlikely that it is a young object since it is not associated with a molecular cloud. It is probably a post-AGB star that very recently left the AGB (since it is an early M-star). The bipolar outflow may have been formed through interaction with a binary companion, although so far there is no observational evidence for such a companion.