I have always felt the Ninth Doctor's regeneration was a bit like what we saw with Eleven in The Eleventh Hour. In that story he regenerates and has to deal with a crashing Tardis. He then meets young Amy and tries to deal with the crack and then he has to go stabilise the Tardis and returns to Amy and deal with Prison Zero. He only finds out what he looks like near end of story when Prisoner Zero copies his form.
For Nine he regenerates after 'destroying' Gallifrey and then when we meet him in Rose he is trying to deal with the Nestene who seem to have been on Earth for at least a few days. He may have been trying to find them from shortly after his regeneration and was too busy to look in a mirror until Rose's flat. Just like how busy Eleven was after his regeneration to stop and look in a mirror.
For Nine he regenerates after 'destroying' Gallifrey and then when we meet him in Rose he is trying to deal with the Nestene who seem to have been on Earth for at least a few days. He may have been trying to find them from shortly after his regeneration and was too busy to look in a mirror until Rose's flat. Just like how busy Eleven was after his regeneration to stop and look in a mirror.