The term 'swift-running bird' can be summarized by three crossword solutions: bustard (7 letters), EMU (3 letters), and OSTRICH (7 letters). Bustards are large, terrestrial birds found in Europe, Asia, and Africa. Emus are flightless birds native to Australia and the second-largest living bird by height. Ostriches are the largest living bird species and are native to Africa. All three of these birds are swift-running, making them suitable answers for the term.