Works in blender 4.0.2 with this exporter: https://github.com/GreenXenith/io_scene_b3d

Notes:

• make an armature, make bones, name them
• select object, shift+select armature, go into pose mode, select one bone, ctrl+p, select "parent to bone"
• if you move bone in pose mode now, it should move the object too
• NB: to force exporter export bones, it seems you must have any animation (seems to be a bug)
• when exporting, go into object mode and select all objects, then export to b3d