The hard X-ray source IGR J11215-5952 is a peculiar transient, displaying very short X-ray outbursts every 165 days. We obtained high-resolution spectra of the optical counterpart, HD 306414, at different epochs, spanning a total of three months, before and around the 2007 February outburst with the combined aims of deriving its astrophysical parameters and searching for orbital modulation. We fit model atmospheres generated with the fastwind code to the spectrum. We also cross-correlated each individual spectrum to the best-fit model to derive radial velocities. From its spectral features, we classify HD 306414 as B0.5 Ia. From the model fit, we find Teff = 24 700 K and log g = 2.7, in good agreement with the morphological classification. Using the interstellar lines in its spectrum, we estimate a distance to HD 306414 d > 7 kpc. Assuming this distance, we derive R* = 40 Rsol and Mspect = 30 Msol (consistent, within errors, with Mevol = 38 Msol). Radial velocity changes are not dominated by the orbital motion, and we find an upper limit on the semi-amplitude for the optical component Kopt < 11 +- 6 km/s. Large variations in the depth and shape of photospheric lines suggest the presence of strong pulsations, which may be the main cause of the radial velocity changes. Very significant variations, uncorrelated with those of the photospheric lines are seen in the shape and position of the Halpha emission feature around the time of the X-ray outburst, but large excursions are also observed at other times. HD 306414 is a normal B0.5 Ia supergiant. Its radial velocity curve is dominated by an effect that is different from binary motion, and is most likely stellar pulsations. The data available suggest that the X-ray outbursts are caused by the close passage of the neutron star in a very eccentric orbit, perhaps leading to localised mass outflow. (abridged).
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