We model gas phase metallicity radial profiles of galaxies in the local Universe by building on the `bathtub' chemical evolution formalism - where a galaxy's gas content is determined by the interplay between inflow, star formation and outflows. In particular, we take into account inside-out disc growth and add physically-motivated prescriptions for radial gradients in star formation efficiency (SFE). We fit analytical models against the metallicity radial profiles of low-redshift star-forming galaxies in the mass range $\log (M\star /M\odot )$ = [9.0-11.0] derived by Belfiore et al. 2017, using data from the MaNGA survey. The models provide excellent fits to the data and are capable of reproducing the change in shape of the radial metallicity profiles, including the flattening observed in the centres of massive galaxies. We derive the posterior probability distribution functions for the model parameters and find significant degeneracies between them. The parameters describing the disc assembly timescale are not strongly constrained from the metallicity profiles, while useful constrains are obtained for the SFE (and its radial dependence) and the outflow loading factor. The inferred value for the SFE is in good agreement with observational determinations. The inferred outflow loading factor is found to decrease with stellar mass, going from nearly unity at $\log (M\star /M\odot )=9.0$ to close to zero at $\log (M\star /M\odot )=11.0$, in general agreement with previous empirical determinations. These values are the lowest we can obtain for a physically-motivated choice of initial mass function and metallicity calibration. We explore alternative choices which produce larger loading factors at all masses, up to order unity at the high-mass end.