Traveler's Gun Rights Act This bill broadens the scope of allowable firearms transactions involving active duty service members and their spouses and individuals who do not have a residence in any state. Currently, federal firearms laws generally prohibit a federal firearms licensee (e.g., a gun dealer) from sell or delivering a firearm to an individual whose state of residence is different than the state where the licensee's place of business is located. This bill defines the term state of residence as the state in which an individual is present with an intention of making a home. In the case of an individual who does not have a physical residence in any state, then the term state of residence means the address of the individual's private mailbox or post office box. In the case of a member of the Armed Forces on active duty, or his or her spouse, the term state of residence means (1) the state in which the member's permanent duty station is located, and (2) the state where the member maintains a place of abode from which he or she commutes to the permanent duty station.