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In private life he was equally respected. For four seasons, 1832–36, he was Master of the Worcestershire Hounds, and Cecil, in his “Hunting Tour,” speaks of him as “a fine sportsman, whose hunting lore was not the less valuable from having been cultivated by the ever celebrated pastor and sportsman, the Rev. William Smith, of Badger, whose pride it was to instil into his pupils the education of gentlemen, with an appropriate taste for fox-hunting.”

— Holden, Captain Robert Mackenzie (1887) Historical Record of the Third and Fourth Battalions of the Worcestershire Regiment. Kegan Paul, Trench & Co., London source

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There were likewise two clergymen who did much honour to the “noble science.” Though not assuming to unbecoming emulation as bruising riders, their steady advocacy of fox-hunting was unremitting, and the names of the Reverends William Bate of Willey, and William Smith of Badger, well deserve to be handed down to posterity. Mr. Smith was the preceptor, or private tutor of the late Mr. Hugh Campbell, a gentleman deservedly distinguished in Warwickshire; and also of Mr. Thomas Clutton Brock, for several years master of the Worcestershire hounds.

— Tongue, Cornelius (1854) Records of the Chase, and Memoirs of Celebrated Sportsmen. Longman, Brown, Green, and Longmans, London. source

Not sure on “bruising rider”, although it seems to be a stock phrase. In modern language “bruising” would be “punishing”, but I don’t think that’s it. From other uses it seems to be a positive attribute. I think it’s bold, brave, fearless, with an implication of skill (otherwise you’d break your neck). Here’s a usage I found online, also from Salop.:

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Even as intrepid a heroine as Miss Marlowe would agree there was no more bruising rider than John Mytton. It was said his abilities were known in every county–particularly his endurance. Hunting was the sport that taxed a rider for jumping various obstacles and “often in weather not fit for man nor beast.” In addition to hunting with his own pack, he would hunt with other packs throughout Shropshire.

“During the period of Sir Bellingham Graham hunting Shropshire, (Mytton) performed several gallant feats in the field. Whilst suffering severely from the effects of a fall, and with his right arm in a sling, he rode his favourite hunter, Baronet, over the park paling of the late Lord Berwick..to the astonishment of the whole field–Sir Bellingham himself exclaiming, “Well done, Neck or Nothing; you are not a bad one to breed from.” — Life of Mytton, Nimrod

The Regency Rake: Endurance source