We've had this watch since about 1973 in a safe deposit box. It is not my style but I love old stuff, my grandfather collected mechanical banks, clocks, etc. but this is the only watch that I know of that ever made it to me. Did a ton of google searching before finding your site and still can't find this exact model.
I believe this is an Accutron 503 with 14K gold back and band. The variation is that while all the Odd numbers are the same symbol, the number 12 on this one is also a symbol (Y) instead of the number. Pardon any ignorance as those symbols probably have names!
The other thing is the serpentine type band. Can't find this anywhere either. Appreciate the help in gathering more information about it. Thanks.
SO, while we try to find the proper name of this beauty, I'm happy to report that the "Y" at the 12 spot on the dial is the ACCUTRON logo. I's a tuning fork! Simply put, it drove the accuracy of the movement.
You are correct about your watch being a 1961 Bulova Accutron "503". That's a pretty cool looking band but I suspect not something originally sold by Bulova (I could be wrong).
There it is! 1961 Bulova Accutron 503.
1961 Bulova Accutron "503" is a good match. That is a cool bracelet.