The narrow-line Seyfert 1 galaxy 1H0707−495 has shown the first clear evidence of X-ray reverberation in which the soft, disc-reflection and Fe-L-dominated 0.3–1 keV band lags behind the hard, continuum-dominated 1–4 keV band by ≈ 30 s. A simple reflection model, however, cannot explain the different amplitudes of variability between the continuum and reflection components in time-resolved spectra. Here we apply a light-bending model (LBM) to 1H0707−495 to determine whether or not it can fully account for both the time-averaged spectrum and observed X-ray variability and time lags. A point-like source is assumed to move vertically from 3.5rg to 8 rg approximately along the rotation axis of the black hole. Photon paths are integrated via a numerical method for each source position to calculate the corresponding direct and ionized reflection spectra from the accretion disc. The source is assumed to move up and down in such a way as to reproduce the 1–4 keV light curve from the XMM–Newton observations. We find that, even though the reproduced time-averaged spectrum generally agrees with the observations, this LBM cannot account for the observed time lags between the continuum and reflection spectrum. Furthermore, timing properties such as coherence are sensitive to the ionization state of the inner disc. We conclude that a more complex model of the source geometry and intrinsic variability are required, and probably one in which fluctuations propagating through the disc are directly associated with the X-ray sources. Our ionized reverberation mapping model is completely general, allowing other scenarios to be investigated in the future. Reverberation signatures are beginning to constrain the true nature of the X-ray source of not only 1H0707−495, but also other active galactic nuclei.