GPA: 4.2
SAT: 1360 (without essay)
No AP courses since my high school doesn’t offer them, but I’ve taken 3 dual enrollment courses (my school doesn’t offer a lot), and about half of my courses are honors courses.
I do theater mostly, and have directed two plays, and I have also had two part time jobs, an internship, and am in NHS. I am also in my school’s chorale.
What do you think my chances are? Should I take the SAT again, or with essay?
If applying RD the sat might be a problem and applying ED will give you a better chance that way. But it also depends upon what major you wanna study.
BU does not take into consideration the SAT essay, according to their common data sheet, so you don’t need to take it with the essay. It wouldn’t hurt to try SAT again if it’s just your first time though, because it usually goes up the second time. But you have a shot! Good luck 
I’d try to retake the SAT! Like traindude1 said, your score tends to go up the more you take it (mine went up 20 points without studying the second time), and your score is on the lower side of the average. You might want to offset that you don’t have APs with a higher SAT score because for them it’s easier to compare your academic ability with other students that way. Best of luck!