Can I get into Boston University with no AP classes?

It is my dream school but I am not sure I can get in. My school is a top public school in my state and has a very rigorous curriculum. I took mostly honors classes and have a 3.7 weighted GPA. I didn't take any AP classes because my teachers or guidance counselor didn't recommend any for me. It was a struggle to get the A's and B's I did get with the honors classes. To give you an idea of how competitive my high school is, even with my grades and GPA I barely made the top 35%. I did get a decent SAT score, 1850. I also made it into the National Honor Society, I have danced competitively with my dance studio for many years and have been a volunteer student teacher in some of the smaller kids classes for a few years. I also play the violin and have been a member of the orchestra all 4 years. I have other various volunteer hours through my church and a teen organization.