bpy.ops.object.parent_set(type='ARMATURE_NAME', keep_transform=True)

vertsToAssign = ob.vertex_groups[parent_bone]

# Assign all vertices of the object to the chosen bone with 100% weight:
mesh = ob.data
for vert in mesh.vertices:
    vertsToAssign.add([vert.index], 1.0, "ADD")