Well, two years ago I applied to Hebrew Bible/Semitics/Ancient Near East programs directly from an international undergrad institution. I applied to 9 PhD programs and 4 masters.
I got accepted by only one PhD (UT Austin) and was rejected by all the rest. Although Brandeis accepted me to their master's program with partial funding.
Concerning the master programs I was accepted by Harvard Div., U of Chicago Div. School and Jewish Theological Seminary. Rejected by Notre Dame.
I'm now enrolled in the Harvard MTS program and reapplying. It seems to me that one's chances don't get higher with a master's degree in hand, since so much depends on the candidates' pool of the year. I'm not even sure whether I'd get in UT Austin again if I applied to it again this time. Also, though I'm doing a master's at Harvard, I don't see any extra advantage when it comes to application. The worst thing with Religious Studies/Bible and the like is that each program accepts 0-3 students a year and they are OK with not accepting anyone into one specific program in a particular year (meaning no one was waitlisted, like Jewish Studies at Harvard, and HB at Brown last year if I recall correctly). So not that I'm being exceedingly pessimistic, but it is possible that if you are not among the top 5-8 candidates among all applicants applying to all major programs, you may end up not being able to get into any program. (If all the programs accept the same people and if some of them don't use a wait list, like what some professors told me when I emailed).
So I'd say, give it a try to apply for PhD programs even if you don't have a master's. And accept the offer if you get lucky instead of reapplying, which feels much worse than the first time. Academically you can always take more courses while you already are in a PhD program so a master's is not necessary in that regard.