

There is a great sticky up top in the forum on the different species, with nice info on each, a video, and updates that have been made scientifically as far as families and names.
https://www.monsterfishkeepers.com/forums/threads/all-bichir-polypterus-species-updated.684410/
According to that we have:
Lower jaws
- P. Endlicheri
- P. Congicus
- P. Ansorgi
- P. Bichir Bichir
- P. Bichir Lapredi
- P. sp. Dabola (supposedly might be officially recognized as a separate species soon)
Upper jaws
"Big 3"
- P. Weeksii
- p. Ornatipinnis
- P. Teugelsi
- P. Senegalus Meridonales (giant subspecies of senegals, so maybe it should be "Big 4"

- P. Senegalus Senegalus (normal senegal bichir)
- P. Delhezi
- P. Palmas Palmas
- P. Palmas Buettekoferi
- P. Polli
- P. Mokelembembe
- P. Retropinnis