What can I do about prolonged bleeding after being on the contraceptive implant for a month?

Patience. I presume you are referring to the implanon. This device is a progestin only contraceptive which carries about a 70% to 80% risk of daily spotting and bleeding that may last for up to 6 or 8 months. There is no effective long term treatment for the bleeding, be patient and it will probably quit eventually.