From my book Complete Irish:
"bh, mh: Pronounce v when broad... In the middle of a word, broad bh/mh are also pronounced v after a long vowel (one with the accent), e.g. ábhar (subject) is a ávar... The sequence short vowel + bh/mh in the middle of a word gives an ow sound as in pound e.g. leabhar (book) is lyowr.
Slender bh/mh are v in all positions."
So if I'm in doubt, I guess v as it seems the most likely.
The Pronunciation of mh or bh varies regionally. In Ulster the General rule is that they are pronounced w when broad and v when narrow. In Munster (as in the Western isles of Scotland) the tendency is to pronounce as v at the beginning or the end of a word and w in the middle. I've never been able to figure out exactly how it works in Connacht.
Check this: http://en.wikipedia.org/wiki/Irish_orthography#Vowels It may look intimidating, but it does help!
The sound you hear is coming from the "R" - it's a quirk in the way she pronounces labhraíonn (in her dialect, labhair is treated as a first conjugation verb, so she says labhrann, even though it is a second conjugation verb, and in other dialects the pronunciation more closely follows the spelling labhraíonn, so the í is pronounced).
You can hear her pronounce labhraíonn in some other exercises for comparison - there is quite a bit of variation (which isn't a bad thing - that sort of variation is natural in ordinary speech), and that "d" sound isn't there:
Labhraíonn sé Gaeilge
Labhraíonn an fia Gaeilge
An labhraíonn tú Rúisis?
Labhraíonn an leon
The way I think of it is, the bh in this case makes a 'w' sound, so it's lah-ww. The R sounds a bit like a 'd' in this accent, so put together, labhr- sounds like lah-ww-d ("loud").
Next is -aionn, which sounds to me like 'ah-on' but the 'ah' is fast, so it kind of just sounds like 'on'. All together, labhraionn --> loud-on (sort of)
Hope that was helpful! Anyone with more knowledge than me, feel free to correct me haha
As pointed out above, there are other examples of this speaker saying labhraíonn that don't have this "D" sound that some of you think is there (I don't hear it).
The second part of the word is not "aionn", it's aíonn with a fada on the í, which should have an "ee" sound, but she is rushing it so much that it's more like "rin" than "reeon".