Hello JRMDR, there are schools that will accept students after three years of undergrad without a bachelor's degree. Sometimes students with stellar credentials will just decide to apply after two years of undergrad for admission after their third year. Since DesiDentist said 95% of matriculants have some kind of degree, these would be the 5% that don't have a degree. I thought JonR on this board who was headed to UConn was one of these students. I know of two students at my dental school who applied and were accepted without degrees. One went back to receive the undergrad degree after the first year in dental school (the school gave it to him, he didn't have to take additional courses), and the other never went back for the undergrad degree. It doesn't make a difference since the second student just graduated from dental school this year.
If you have the credentials and don't want to hang around in college anymore, I would say go for it! Apply to dental schools after your second year, it won't hurt. I began dental school without an undergrad degree. At that point, I really just wanted to start dental school. I was working toward a biology degree, which in my opinion, was an unmarketable degree anyways, so I didn't see the need to stay senior year and take courses like marine biology and ornithology. I knew dental school was my ultimate goal and I wanted to start taking courses like Endodontics and Biology of Dentistry. It sounds like you have what it will take to be a competitive applicant. Good luck!