He was the eldest son Sir George Bingham, 2nd Baronet and his first wife, Anne Partiger.
[citation needed] In 1692, Bingham entered the Irish House of Commons for County Mayo, representing the constituency until his death in 1714.
[citation needed] On 4 September 1677, he married firstly Jane Cuffe, daughter of Sir James Cuffe, he married secondly Lettice Hart née Vesey widow of Merrick Hart.
[citation needed] He died childless and was succeeded in the baronetcy by his younger half-brother George.
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