Daughter of the first English Collector of Customs in the Isle of Man, and wife of Captain William Bligh.

Her father was Richard Betham, LL.D. On the completion of the sale of the Island, the government agreed at the Duke of Atholl's request to retain every officer of his appointment except the Collector of the Customs, and that office was conferred on Betham. He held it until his death in 1789. A contemporary called him a gentleman whose erudition was truly respectable, and to whose politeness and friendship he was highly indebted.

Her mother Mary died in 1766, aged forty-two, and is buried at Onchan. Mary's father was Neil Campbell, Principal of Glasgow College from 1728 to 1761, which is how the family came to be connected with the Campbells of the West India trade. A Margaret Betham buried at Onchan in 1783 may have been Richard's sister, come over to keep house for him, since he was left with two young daughters, Elizabeth and Anne.

Elizabeth married William Bligh at Kirk Onchan on 4 February 1781. Some accounts of the marriage give her name as Betty. A daughter of the marriage was baptised at Douglas in 1784.