The end of the rope captures the bight. Upon capture the end of the rope forms this special bight. Finally, the bight is pulled through loop. It reverses a prior step. The end of the rope follows. Now this is the bowline.
The second image above is the completed bowline. It was formed by capsizing the slip knot. Thus a bowline can be formed from a slip knot. The opposite is true. A bowline can roll into slip knot and fail. To stabilize the bowline, it's common to tie off the end of the rope. Here the Yosemite tie-off is being used. The end of the rope traces the up-rope. Finally, a double fisherman provides additional security.