If the reason you'd like to use Bembo is your personal preference for »Renaissance« or »Humanist« typefaces, i.e. ones that bring across the aesthetics of the 1400s and 1500s -- there's two typefaces you should have a look at:
(1) the various digital renditions of Hermann Zapf's Palatino that are around, and (2) Robert Slimbach's Minion. Depending on how you look at a typeface (what aspects you're sensitive to), they may or may not be »close equivalents« to Bembo.
But since you seem to have to deal with a lot of math in your typesetting, your choices are somewhat limited anyways. I'd say the two fonts that best meet your three main requirements, that is
- share Bembo's look, to some degree
- be prepared to be used for math purposes (this is highly non-trivial)
- be readily available at no $$$ (right?)
are (1) TeX Gyre Pagella, which is a rendition of Palatino, ready to be used in *TeX, and equipped with math capabilities (math experts, feel free to correct me) -- and (2) Minion Pro, in OpenType format, of which eight cuts come as a give-away with Adobe's Reader.
This is how, as a non-Xe or Lua user, you would invoke the Pagella font:
This is what Minion looks like (middle). I like it a lot more than Palatino, but that's personal taste I guess. It is, obviously, also closer to Bembo than Palatino is. There's the famous
minionpro package which helps getting the font ready for use in pdfTeX. Plus there's the
mnsymbol package to provice math symbols that go along better with a Renaissance face like Minion than do the standard symbols designed for the Classicist Computer Modern face.
For $108 by the way, you can license Bembo Book, (Regular, Regular Small Caps, Italic -- you wouldnt want to use a Bold with a 1400s typeface). If you really like Bembo and are looking for a professionally-crafted font that's versatile enough to be used in your life after the PhD, this might be something for you.