A bawbee was a Scottish halfpenny. The word means, properly, a debased copper coin, equal in value to a half-penny, issued in the reign of James V of Scotland.  The word "bawbee" is derived from the laird of Sillebawby, a mint-master. That there was such a laird is quite certain from the Treasurer's account, September 7th, 1541, "In argento receptis a Jacobo Atzinsone, et Alexandro Orok de Sillebawby respective." 

It was metaphorically used for a fortune by Sir Alexander Boswell, the son of the more famous James Boswell, the biographer of Dr. Johnson. It occurs in the song of Jennie’s Bawbee  

Quoth he, "My goddess, nymph, and queen,
Your beauty dazzles baith my e'en",
But deil a beauty had he seen
But Jennie’s bawbee

Sir Alexander took the hint of his song from a much older one:-

A' that e'er my Jeanie had,
My Jeanie had, my Jeanie had,
A' that e'er my Jeanie had
Was ae bawbie
There's your plack, and my plack,
And your plack, and my plack,
And Jeanie's bawbie.

Brewer's lists "Jenny's Bawbee" as meaning a "marriage portion".  The term "bawbee" was still being used in Lowland Scots in the 20th Century, and may still be in minor use somewhere.