He was the younger brother of Sir Miles Stapleton and the third son of Sir Gilbert Stapleton (died 1321) and his wife, Agnes (or Matilda; 1297/8-1348), daughter and coheir of Brian, Lord Fitzalan (died 1306), of Bedale and several other estates in the same county.
Bryan served under the banner of William Montagu, earl of Salisbury, in France in 1359-60 and, very likely, before that date as well.