Late fiftied early sixties... That's a Sears bike that was built in Little Rock, Ark. by the Murray of Ohio manufacture. [they moved from Ohio to Ark. in the early 1950s]. This is a VERY CLEAN specimen... even the light has survived superbly; they usually do not. I may be a tight-wad; but this is a women's bike with little to no market... I would begin to worry about me if I spent $50.00 on it. There are folk who really like these tho... and this is a gem! It would be an example to KEEP in a large collection... just not much value.
How do I know it's a Murray? Look at rear axle nut and bottom fender brace above it; there is a pointy extension of the BLUE frame from the axle nut back... kind of a triangle, it's a Murray! On the other side of the bike; locate this same pointy piece; remove fender brace bolt/washer and axle nut/washer; now you can see MOx xxxx, etc. This is year data, Model designation, and serial number. Copy them down and Google Murray bicycle Serial Numbers; you will find several choices/sites where you can see what year [MOx] I believe will tell you. The four digit number group is the Sears Model/catalog number. The longer number grouping is the serial number. Another option: find Sears catalogs from that era and search the bicycles.