Brigtoune 1681 Retours (Fife) no.1198 [see Bonnington SLN]
Brigtown 1798 Sasines no.5192 [Brigtown and Curriesholl called Bonningtown]
Sc brig + Sc toun
The eponymous bridge is presumably over the Black Devon, probably just upstream from Cultmill. But see also Balgonar SLN and Bonnington SLN.
This place-name appeared in printed volume 1