I would just write a Makefile and leave the Vim settings alone. In general, the makefiles I use are pretty dumb, but even they take care of BiBTeX, and I usually compile three times. You can do much better with more effort. Less effort example -
myfoo.pdf: myfoo.tex pdflatex myfoo pdflatex myfoo bibtex myfoo pdflatex myfoo
(except that you need to use tabs, not spaces, and I have not tested above, and I myself do not use pdflatex, so I expect errors). If you don't like Make (and who really does), then you can use some other similar build tool, then install makeprg for it. I have never tried this.
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