Did Hitler die in his bunker or escape Berlin?

Yes, he committed suicide in the bunker beneath the Reichkanzeleri building in Berlin on April 30, 1945. Soviet Army troops wer closing in on his position, and were only a few hundred metres away at the time of his death. He took a cyanide pill, and then shot himself.
After he and his wife committed suicide their bodies were taken outside and burned. Hitler had hoped to be cremated so that his body was never found, but there was not enough fuel left to fully incinerate the bodies. His remains were found by the Soviets a few days later.