That looks just like my watch the band is different but the actual markings on the case with the diamond chips and three curved marks on each side of the face are just alike. I am also looking for the value of this watch I have a second one as well so from what I found mine is a 1962 la petite watch. If you find anything else out please let me know.
Your watch looks to be a Goddess of Time. Edit to say the two-tone case is the "B" per Ken's research.
1958 Bulova Goddess of Time "B"
Goddess of Time "B" works for me. Good catch!
Here are a couple ads for the 'B' (1954/1955)