What is the cost of mailing a 10 lb package of a live bird via USPS?

here is the info for the postal regulations; for the cost, you will need to contact the usps -

526.4 Adult Birds
526.41 General
Disease-free adult birds may be mailed domestically when shipped under all applicable governmental laws and regulations, including the Lacey Act, the Endangered Species Act (ESA), and regulations of the U.S. Department of Agriculture, U.S. Fish and Wildlife Service, and any state, municipal, or local ordinances. Mailers must comply with all applicable governmental laws and regulations, including the Lacey Act, the Endangered Species Act (ESA), and regulations of the U.S. Department of Agriculture, U.S. Fish and Wildlife Service, and any state, municipal, or local ordinances. Mailings must also be compliant with the requirements provided in USPS Publication 14, Prohibitions and Restrictions on Mailing Animals, Plants, and Related Matter, Chapter 5. In addition, each container or package must be marked as required by U.S. Fish and Wildlife Service under 50 CFR 14. Adult birds must be properly packaged and able to sustain shipment without food or water because liquids, moisture, and loose foodstuffs can cause damage to the shipping container, other mail, and Postal Service equipment during transport.
526.42 Mailability Requirements
Adult birds are mailable only when sent under the following conditions:
The shipment is mailed using Priority Mail Express service.
Each bird must weigh more than 6 ounces and no more than 25 pounds.
The number of birds per parcel must follow the container manufacturer limits.
The mailer must secure containers approved by the manager, Product Classification (see 214 for address).
A mailing container must be used that is constructed by a USPS-approved manufacturer listed on the RIBBS website at http://ribbs.usps.gov.

not sure you can do that; ask a pet shop

you expect a live bird to survive us mail? most likely not even allowed to ship live birds

visit the website for actual info Free