If I can pitch my two cents in -
The blurry image, to my eye, does not show internal bubbles - this looks more like surface impact damage on glass.

Bakelite would be the absolute last thing I would suspect. Phenolic resins would have to be machined into the melon shape - very labor intensive. And though it is possible to make water clear phenolic resins, I have never encountered any that were made into jewelry. The tendency of phenolic resin to turn yellow or brown over time "should" be apparent in most phenolic jewelry items (but this depends on the exact formulation used).

Most of the "crystal clear" vintage plastic jewelry was made from Lucite (also known as acrylic). So yes, the melon beads could be Lucite. But I can't tell from the photos.

The other clue that caught my eye - the inside of the hole on one of the melons is smooth and clear. That would indicate to me that glass is the strong possibility. Maybe ask if the holes are tapered - that would indicate tong molding.

Any chance you can request better pictures, and if not, can you ask to return the beads if they are not glass?