It's bodingly in both the NNSB and Appleby/Fowler. A perfectly good word; though nowadays we'd say forebodingly, perhaps.

According to Chappell, the Rev Felton was prebendary of Hereford; the tune began life as part of one of his concertos, and was afterwards published, with variations, as Felton's Gavot. 1728 is too early a date; Felton was only about 13 at that time. Generally thought to be 1740 or later. The story about the tune being played when the rebels left Manchester, and another that it was played at the execution in Manchester of Jemmy Dawson in 1746, are from Chappell. He may have had evidence, but according to Kidson none survives.

Several songs have been set to it. A song called Farewell Manchester: A song made on the Peace appeared around 1748, but doesn't seem actually to have mentioned Manchester; Chappell thought the original song of that name to be lost. Oxenford's new words to the tune appeared as "Prince Charles Stuart's farewell to Manchester in 1745. Old English air with symphony & accompaniment by G. A. Macfarren. (New words upon the old subject by J. Oxenford.)" The British Library copy is dated 1883, but original publication may have been a bit earlier, as Oxenford's dates are 1812-1877.

William Chappell, Popular Music of the Olden Time, 1859, pp. 682-3.

Frank Kidson, entry in Grove's Dictionary of Music and Musicians: Farewell Manchester.