What you hear is largely true, Nassau isn't Abaco or Andros by a long shot; but it is possible to catch bones there on the fly.
The north side is not suitable, but there is a flat on the south side of the island, if you look on google maps it's identified as Bonefish Pond National Park. Between there and the dredged channel you see @ Venice Beach is a fishable flat. Like you, I was on vacation with the family and wanted to fish but not take more than a half day away from the family. I called an outfitter I'd spoken with before (who owns a lodge on Abaco) and he arranged for an off-duty guide from his Abaco lodge to take me out for a half day - on a borrowed boat. He was moonlighting. Anyway, we did come across some waders and offered them water - they were from France and were wading south of the old Bacardi Rum plant... the only other fishermen we saw. The fishing was good; but I don't think tarpon are a possibility based on what I learned. We drove through some woods and dropped the skiff from shore here 24.982893, -77.444866
A few years later I was in Abaco on a trip and recounted the story to the lodge guides and they all died laughing.... apparently the guide who took me later stole that boat and ended up in prison. So, there's that too. Bottom line - GOOD for bones, probably not, certainly compared to Abaco, Andros; POSSIBLE for bones, yes, at least 8 years ago with some effort. YMMV. Good luck.