How would you get out of a bomb shelter after an atomic bomb blast?

You would need a radiation survey meter (a geiger counter will NOT work for this) to periodically check the outside radioactivity levels on very short periodic trips outside the shelter. Once the radioactivity is low enough (which could take a few weeks to longer than three months) you can permanently leave the shelter.

If you want more information read Dean Ing's novel "Pulling Through" which includes an appendix in the back describing how to make all the items that the characters in his story built from everyday household materials and use them if needed to survive in a similar nuclear war situation.