Bakelite is a thermosetting plastic so once "cooked" it is not affected by heat up to several hundred degrees. Other plastics used for radio cases (mostly starting in the 1950s) were thermoplastics which melt at a fairly low temperature.
Touch a hot soldering iron to an inconspicuous spot on the case bottom- if it melts, it's thermoplastic (styrene or related material); if it doesn't, it's bakelite.
Bakelite is also much harder than thermoplastic and will not scratch easily if you try to gouge it with a sharp steel point.