As noted by Torrie, Beatrice was born in Port Bannatyne in Bute in 1887, her parents being Duncan, a fisherman, and Betsy (Elizabeth) McBRIDE, who were married in Kilfinan in 1876, just across the water from Bute.
The 1876 marriage shows the parents as Allan LIVINGSTON and Janet LIVINGSTON MS McINNES , and Alexander McBRIDE and Isabella McBRIDE MS McALISTER.
Janet LIVINGSTON MS McINNES died in 1855 in Lochaline in Morvern parish.
Allan died in Kilfinan parish in 1867, aged 78, parents Duncan LIVINGSTON and Mary CAMERON. Back to this generation I can't see a connection to the missionary David LIVINGSTON, - but that's not to say that there isn't a connection in earlier generations !
Wullie