Can't do IPA on my phone, unfortunately. Most of the time I've heard "mraw/mrah" and, in searching a while i found that some people say "m'noo". I'm far from fluent, though, so I can only say what I've heard. I downloaded an app "How to Say: Pronunciation App" and teanglann.ie really helps.
Bean has the most irregular declension of any Irish noun, as it preserves a lot of historical weirdness. In Proto-Celtic the (nominative) singular is reconstructed as *benā but because of weird historical reasons the first syllable gets deleted in most other forms like the nominative plural which is thought to have been *bnās. During the transition into Old Irish the endings were dropped and the "b" in *bnās turned into an "m", yielding mná.
As for why the "n" is pronounced like an "r" this occurs wherever "n" follows a consonant except for s in all dialects save for Munster and the Aran Islands. This change must have happened along time ago, as it also occurred in Scottish Gaelic and Manx and there's evidence of its former presence in parts of Ireland that have long been English-speaking.