I've shipped to contests.
Do not use USPS (postal service) as there are federal regulations against shipping alcohol. not to mention that if a postal carrier is injured by your package that is a major crime.
additionally some states have laws about shipping alcohol across their borders, just FYI. I don't think anyone is really checking all that closely.
UPS or FedEx have policies against shipping alcohol but don't ask, don't tell seems to work here most of the time.
package well so there is no chance of two bottles contacting each other. Ideally include at least one layer of moisture barrier to prevent leakage should a bottle break.
oh, it's expensive too.