The purpose of bathing the bracelet in (baby) oil is not to make it shinier, but to make the bracelet smoother. Rep bracelets often feel rattly and not smooth when moving the links.
If you put it in baby oil for a few hours, moving the links back and forth a little in between, it will feel great and smoother. Some people say that it feels more gen like, especially on Rep Rolex bracelets, which I can personally confirm.
I at least give all my oyster bracelets an initial oil bath, it's definitely worth it.
You just have to clean it very well after the oil bath, I use microfibre cloths very well for this.