Well an M.A. or M.S. will be your minimum. On average this can take between 6 to 8 years (this includes going through your undergraduate work). If you choose to go on for a Ph.D., this can take another 3 to 5 years depending on how much time you devote to finishing. In order to become Board Certified, you'll need the Ph.D. and several years practical experience.
If you you go on be a forensic anthropologist, here are a few suggestions
1) Taking classes outside of your major can be beneficial. Archaeology field schools will teach you about excavation and survey. These are two big skills that should be mastered as they are crucial to the recovery phase. Cultural anthropology and sociology classes, especially those dealing with mortuary practices, can help you learn about how people bury their dead. Statistics will help you to be read and understand the lierature. Anatomy (especially gross anatomy) will help you familarize yourself with the soft tissue. In my experience, it is equally important to know what goes through a foramen (hole) as it is to be able to idenitfy the structure. Other helpful classes: biology, chemistry, geology (this should include soil sciences), zooarchaeology (learn to id animal remains), kinesiology/biomechanics
2)Join the applicable associations. The American Academy of Forensic Sciences and the American Association of Physical Anthropologists have yearly meetings where posters and presentations are given. Presenting at these conferences will help to get your name out there and will allow you to network.
3)Get working in the lab early. Your university will have a physical anthropology lab. Volunteer there. This will help you get to know the other students and allow you to practice your osteology
4)Make friends with the local medical examiner's office. If you prove yourself to be a competent student, they might be able to use your help in body recoveries
5)When you get your M.A. or M.S. apply to be a volunteer at Disaster Relief groups like Kenyon, Forensic Archaeology Recovery (FAR), Physicians for World Peace, and the United Nations. Sometimes you might be given the option to head to places like Iraq, Rwanda, Croatia, Serbia to work on mass graves. As thrilling as these places might be, give it a good long think before you agree. A single body can be traumatic; a mass grave can be devestating.
Anyway, that's my advice. In my opinion, it's a wonderful field. If you work hard at it and diversify you studies, you'll be better off than most.