Easiest way from Undead Crypt to Majula (no bonfire)
Solution 1:
There's only one way back: the way you came from. Go back to the crypt's entrance, up the lift, back through the shrine of Amana, up the lift, back through Drangleic Castle, down the path to the Shrine of Winter, in the Shaded Woods fork area, then finally back to Majula.
After discussion with klm123, it appears the door in the middle of the building between Majula and Shaded woods takes about 10 minutes to shut back down. You can then pull the lever again and the door to Majula will open.
See this map for reference 