Presumably he was in another part of the building, or had left my another exit to the one Rose used, at the time the bomb went off. (the Doctor didn't get to be 900 years old by being stupid, y'know!)
I always figured he'd parked the TARDIS in the building somewhere and used that to escape.
The TARDIS was parked against a shop some short distance away. Rose passed it as she fled after the explosion (this was shown on screen), though she did not notice it and would have had no reason to connect it with the Doctor, even if she had. The explosion did not destroy the whole building and there was a delay between Rose leaving Henrik's and the explosion, so the Doctor would have been able to take cover from the blast, then leave the building before the fire took hold.