Reversing black & white was a very common procedure going back a bit – it’s not widely known that most B&W films can be successfully reversed to give a B&W transparency. The best results will usually be with slow and medium speed films, however.
The procedure is similar to reversal processing colour transparency film. A first development stage produces a black and white negative. A bleaching bath then dissolves this away, and the remaining sensitive silver in the film is fogged and redeveloped to a positive image. Fixing and washing is as normal.
As with colour E6, using film in this way limits the exposure latitude, there is far less tolerance to over & under exposure. But a plus point is that the graininess of the film can be expected to be much finer than normal, as all the larger grains that initially record the image are bleached out, and the smaller grains in the emulsion are those that go to form the final image.
Similarly to colour reversal, speed can be ‘pushed’ by increasing first development, and pulled by decreasing it, the practical limits are about a stop or two.
If you want to tackle producing the baths yourself the method available detailed on the Ilford PDF is up to date. This needs a few chemical as well as standard developer & fixer;
Potassium Permanganate – various suppliers on Ebay
Sodium or Potassium Metabisulphite – various suppliers on Ebay
Sulphuric acid – not so easy as the other two. Have a look at proprietary drain cleaners, there’s quite a range from the big chains like Homebase & B&Q. Although some are caustic soda, some of them are quite concentrated sulphuric acid which when diluted will be fine for use in the permanganate bleach. In alarmingly small print one should find the % strength, and as always be very careful when diluting, putting sulphuric acid into water & never water into the acid.