Burke (Bourke, De Burgo), Hugh (c.1592–c.1654), catholic bishop of Kilmacduagh, was born in Co. Galway and had at least three brothers, including Archbishop John Bourke (qv) and Oliver, a Dominican friar. He studied at St Anthony's, the Irish Franciscan college at Louvain, received the tonsure by 1613 and was ordained priest on 18 February 1617 at Malines. He held a series of offices within his order, throughout Europe. On 16 February 1618 he was appointed professor of philosophy at Louvain, was appointed guardian of the college in March 1622 and was lector emeritus in theology there by 1623. He appears to have been named as commissary visitor to Ireland in 1623, being in the country in the following year. In 1625 he was sent to the province of Aquitaine to reform studies there, also teaching theology. In 1626 he set off for Spain with Archbishop Florence Conry (qv), arriving there in 1627, acting as secretary to Conry but remaining in Spain until 1634, well after Conry's death. The 1634 general chapter at Toledo named him provincial of Denmark, and in the same year the Franciscan minister general appointed him commissary general of the order's Irish colleges at Louvain and Prague. He may have had little success in promoting the Danish mission, and spent the next several years largely between the two colleges, though he may also have acted as vicar-general to the Irish forces in Spanish services in Flanders at this time. He was keenly interested in contemporary theological debate, and supported Conry's interpretation of Augustinian doctrines in the debates surrounding the emergence of Jansenism.
With the outbreak of insurrection in Ireland in 1641 Bourke played a prominent part in facilitating the dispatch to Ireland of war materiel and of Irish soldiers in foreign service, most notably Owen Roe O'Neill (qv). On 28 November 1642 the confederate supreme council in Ireland appointed him one of their representatives to the emperor and to various Catholic authorities, civil and ecclesiastical, in northern Europe; on 7 August 1643 he was also appointed agent to the Dutch United Provinces. The bulk of his activity centred on Flanders, where he sought logistical support for the confederate war effort. On 12 January 1645 he was transferred to Spain, as representative to Philip IV. He travelled via Paris where he met Archbishop Rinuccini (qv), papal nuncio to Ireland, and Richard Bellings (qv). He had been recommended by the supreme council for promotion to a bishopric on 13 June 1644, was recommended by Rinuccini the following year and was appointed bishop of Kilmacduagh on 1/11 March 1647. His brother John had, however, sought to have him as his successor in their native diocese of Clonfert, with Kilmacduagh going to a third brother, Oliver, who had acted as vicar apostolic of that diocese since 1629. He remained in Spain until 1648, his brother Oliver acting as vicar general of the diocese.
The turn of events caused great resentment among the family, and possibly contributed to their opposition to Rinuccini's attack on supporters of a truce between the confederates and the Protestant commander Inchiquin in 1648. On 17 January 1649 Bourke gave his support to the recent peace signed by the confederates and the marquess of Ormond (qv), and appears thereafter to have followed the political line of his brother John and of the marquess of Clanricard (qv). Having taken up residence in Galway, he was present at its fall to Cromwellian forces in April 1652. Thereafter activities are unclear, but in 1653 he seems to have travelled to London, apparently to facilitate communication with Rome on behalf of the Connacht bishops. He may have died in London shortly thereafter.