As Viscount Mayo in the peerage of Ireland, he had a seat in the Irish House of Lords from 1649 until his death.
The son and heir of Miles Burke, 2nd Viscount Mayo, by his first wife Honora, Bourke was reported to have been educated at Oxford, which at the time was open only to Anglicans.
As Sir Theobald Bourke, he was one of the two Members of Parliament for County Mayo from 1640 to 1649, when he succeeded his father in the Lords; he distinguished himself in the Royal cause during the Wars of the Three Kingdoms.
His daughter Maud married Colonel John Browne who built the first Westport House.
[2] In December 1652, Mayo was found guilty by Cromwell's High Court of Justice in Connaught, of murders committed in the 'late rebellion', and was “ shot to death,” 15 January I652/3, at Galway, and buried there.