Hitler is drugged by his doctor, Theodor Morell, at the request of his subordinates and is dragged out of the bunker to his mountain fortress. Berlin is abandoned shortly thereafter and the nazis hold off for as long as they can, regrouping whatever forces that can still move into the mountains.
The area is eventually overrun by Allied forces. From there, one of two things can happen. One is that he is captured by the Allies and placed under arrest. Whether he stands trial at Neuremberg depends on his health.
The other scenario is that his most loyal subordinates drug him again, disguise him, and blend in with the refugees heading wherever (that means shaving Hitler's moustache and all his hair, perhaps using makeup to make him look a little different.
However, if Hitler is dragged out of Berlin, it's very questionable on whether or not he'd even want to continue fighting. The loss of the capitol would be a devastating blow to him and his ego. The only effect of leaving Berlin might be his suicide being delayed and in a different place. It might also allow someone like Goering to assume command (like he tried to do OTL) and co-ordinate a defense for as long as he could.
Ultimately, Hitler's escape would have meant nothing other than he gets to live out the rest of his days in painful suffering as his multiple diseases slowly eat away at his mind and body until he eventually dies. With the war essentially lost (and to Hitler, with Berlin lost) he would likely have finally lost the will to fight.