Budapest semesters is fun. If you want to, do it. Doing well in those courses will reaffirm your math preparation.
Did you work with a stats professor at Duke? If so, get a recommendation from this person if possible. Duke has a lot of well-known faculty members in Bayesian statistics.
If you like computational modeling and Bayesian statistics, then I would emphasize this in your applications. You might consider applying to schools with a focus in this area, e.g. Duke, Columbia, UCSC, UCI, UT Austin.
The competition is pretty stiff, so definitely apply to a range of programs. But you have a lot of valuable experience (the REU in Bayesian statistics, the computational experience, the mathematics background), so I think you'll be all right. Definitely emphasize the strengths I mentioned in your SOP and mention any areas you think you're interested in so long as there's some intersection with work the faculty are doing at the school you're applying to. That'll play well at a lot of departments.