You may apply for the HPSP if you are U.S citizen. In addition, to be eligible for the 4 year, you'll have to apply for it the same time you apply for dental school. In the case of the 3 year scholarship, you'll apply for it the fall of your d1 year, sometime in October I believe.
Forgot to mention, if you have any obligations to the Army, you'll have to serve those terms before you can be commissioned into this program like, ROTC or reserve. In that case, you'll need permission.