Remember that it didn't used to be illegal to export antiquities from their home countries. In the 18th and 19th centuries, thousands upon thousands of artifacts came to the US legally as tourist souveniers. What came here legally then, is still legal to own, although morally, yeah there may be a guilt factor, and some artifact owners do eventually return their artifacts to the countries of origin.
Look at your ring for signs of finger wear on the band, it may be thinner where a human finger would bend around the ring. However if it was grave goods, it would have virtually no wear, since they weren't worn during life in most cases, but may have corrosion from embalming, depending on where it is from. Yours looks like it was worn and was not a grave item.
Most bronze rings are pretty cheap and faking one isn't worth the effort for a small profit. From the photo, yours looks like it has genuine wear and patina. The style is very similar to a lot of ancient bronze rings. I'm not an expert, but an enthusiast, with a small collection of ancient Egyptian and Roman artifacts. I can't say much about the cross, although a lot of the Coptic crosses look similar, and I couldn't say if the ring has a floral design or a cross. It would depend on where it came from and if the seller has disappeared, it is hard to say if what he said was true or not.