it seems impossible to assign spear thrower or grenader to a basher.
cue tells that the assignment worked as a basher quickly falling or such after an assignment will immediately throw a spear/grenade
Confirming that this is indeed a bug, not an intentional decision. (The fact that you can assign them to miners, fencers and diggers should have already given this away. :P )
Fixed in commit b28f4fb.
I discovered that the throwing skills also cannot be assigned to a Laserer. This is fixed in commit 8e313db.