I've never heard of Bell but it's not one of the formal military watch producers from WWII.
That said, it certainly looks to be from the 40s or 50s. The patina of the dial/crystal, the style of the hands, case, etc. all are period. It must be what, 34mm? Any idea of what the movement is?
I recently picked up a redialed RCAF WWII watch that is powered by an AS 894 movement, and the case seems to be an oddity, an E. Morf. I say odd because Roamer bought out the rights to use the E. Morf case, but they typically used their own prorprietary movement, and mine dates to the fall of 1941 to the spring of 1942. So Roamer might have used the AS movement as a stop gap until their in-house was ready. The redial was done in 1967 when the RCAF serviced and updated all service issued watches... so that tells me the owner was career air force.