They often need assistants to help with the mail. Try hand decorating the outside of your envelope with stamps, stickers and use a gold pen to write the address. Send poems or stories or a little something handmade, like a bookmark. Tell them how you connect. No, don't write on the outside with lipstick, it will smear.
Stars get lots of mail and are awfully busy.
Keep your letter to one page if possible. Put your address on the letter Envelopes and letters get separated, so be sure your address is on your letter as well as on your envelope. If you want a big, signed picture, send an eight and a half by ten envelope with postage on it and your address. You can almost always reach somebody famous through the place they work for. Bands have record labels.