skin_cluster_print

import pymel.core

SKIN_CLUSTER_NAME = 'skinCluster1' # <-- Replace with 'name_of_my_skincluster' but keep the quotes!

# Get the skin cluster from the shape node
skin_cluster = pymel.core.PyNode(SKIN_CLUSTER_NAME)

# Get the objects associated with that skincluster (mostly bones)
influence_list = skin_cluster.influenceObjects()

# Print that to the display and the script editor
print_string = 'Objects (bones) associated with {0} : {1}'.format( skin_cluster.name(), len( influence_list ) )
pymel.core.headsUpMessage( print_string )
print print_string

bone_list_string = '\nBones Associated : START-------- \n '
for bone in influence_list:
    bone_list_string = bone_list_string + bone + '\n'
print bone_list_string + '\nBone Associated : END--------'

Replace skinCluster1 within the quotes with whatever the name of your skin cluster is. You can easily find that in the channel box with the mesh selected. It should be skinCluster1 by default, so unless you changed it, this script should be good to run out of the box.