It is important that you be the one to do the necessary research with regard to the airline restrictions, custom/import laws about bringing the budgie into the new country, etc.
Additionally, you need for determine if the country (which one??) allows budgies to be brought into that area from the U.S.
Do not expect your parents to do this for you.
You are old enough to handle the responsibility and showing your parents you have the maturity to take the initiative will go a long way.
Additionally, you should be making arrangements to cover the costs yourself of taking the budgie by airline.
If you do not have a part-time job, try to get one.
Save any money received as birthday or holiday gifts to use for the expense of transporting the budgie via air.
Recognize that your budgie might need to be transported by a different airline that the one you are traveling on -- you'll have to check with various airlines after determining the custom/importation regulations of the destination country.
Make things as easy on your parents as possible and they will be more likely to honor your request to bring the budgie when you move.