I wouldn't fly with it - as many airlines won't even let you check one as baggage.
I would remove the buttstock and pack/bubblewrap both pieces separately in a short box, then mail it to myself (insured) - all perfectly legal under Federal Law.
USPS also has delta-shaped/cross-section Priority Mail shipping tubes, 36" long, that the broken-down & wrapped rifle will fit into. (Available FREE, @ many P.O.'s)
USPS Priority Mailed, to your home, should run about $25
.