In 1945 there wasn't a large body of technical knowledge on supersonic flight when the design of the Bell X-1 was formulated. Many engineering and design decisions had to be made based on the best possible estimates of the aircraft's performance. The fusleage's shape was the end product of the study of the .50 caliber bullet, as it was known to be stable at supersonic velocities. Bell's engineers tried to fill in the data gaps on supersonic flight by observing objects known to fly at supersonic speeds- in this case, the .50 caliber round. Discussions with ballistics experts concluded that little was known about the aerodynamics of the round after it was fired, but since there was no question that it was stable at high speeds, its shape formed the basis for the X-1's fuselage.
Source: Bell X-1 Variants, Aerofax Datagraph 3 by Ben Guenther and Jay Miller. Aerofax, 1988, p6.