From Bachelors Degree in Public Health to PhD/DrPH

What are my chances of getting in to a PhD program straight out of my undergrad? I have a strong mix between As and Bs. My school allows undergrads to take grad courses, so I plan on taking grad courses my senior year. I have a lot of public health work/volunteer experiences. I have not published a paper. I also go to an Ivy League, which may give me an upper hand in some cases. I do realize that an Ivy League education is not the golden ticket though. I am just hoping that it makes me look slightly more impressive.