I would date your dress as early '60s but the late '50s could be correct, as Dior would be fashion forward.
I wish that I could handle your dress because it confuses me: as Jonathan said, it's been altered. The bust has been taken in, but the beadwork is sewn over the alteration so either it was added after the work was done, or it's an applique and the alterations sewer unpicked and resewed them. Also, I would expect a facing at the neck and arm openings - in any evening dress of this time, much less one by Dior. The presence of binding doing the job of the facing suggests another alteration: for example, the neckline was changed and/or the sleeves were removed. It's not even a matching colour, which suggests that the seamstress wasn't very skilled or equipped.
In any case, you made a very wise purchase: even with the alterations and updatings (?) it's an extremely reasonably priced gown. By the way, I would call it hand finished rather than hand sewn, as it's likely to be mostly machine sewn.