Apparent trill in the "br" of "bridge"

Araucaria's comment pointed me in the right direction, specifically this line:

for those people who have a labiodental flap or labiodental approximate for an /r/, which is quite common now in so-called RP, there is often a small bilabial trill, I think, in words that begin with a bilabial plosive

In some dialects (particularly of British English), R can be pronounced as a labiodential approximant [ʋ] (see Wiki), a process known as R-labialization. As Scobbie (2006) notes:

With heavily labialized /r/, bilabial trills corresponding to the clusters /br/ and /pr/ can even be found.

Unfortunately, Scobbie does not cite any sources for this claim, so all I can say is that you and Araucaria are not the first to notice this phenomenon.