The Burning of H.M.S. "Bombay" at Montevideo, and the successful exertions of Capt. TROOP in saving the officers and men. - A despatch from Admiral Elliot and several officer's private letters give us fuller accounts of the destruction of the "Bombay", the Admiral's flagship which was burnt off Montevideo 13th Dec. with the loss of nearly 100 lives. ... From a private letter received by us by the last English mail from Capt. A.G. TROOP, master of the brig "Water Lily", owned by J.V. Troop & Son of (St. John) city, dated Montivideo, Dec. 20th, 1864 - "We picked up over 200 officers and men belonging to the burning ship. As I saw her I crowded all sail, including studensails and made for the place of disaster. I worked the "Water Lily" round and round the burning ship, and picked up boat-load after boat-load of her living freight. Among them her captain and about 18 other officers and some 184 petty officers and men, many of whom were in nature's clothing only. The captain came up one side with a boat's flag tied round his waist and others with their legs stuck through their shirt sleeves. A good many were badly burned. We bound up their wounds and provided them with such articles of clothing as we could muster, using shawls, capes, night dresses and in fact everything that would cover their nakedness; and a more thankful set of half-drowned, half-burned, distressed human beings, I hope never to see again. So that, to use a Yankee phrase, I am 'cleared out'. A day or two ago, the officers came on board in a body, headed by the commander, and tendered to Mrs. TROOP and myself their hearty thanks and assured us we should hear from them again and from higher quarters. This morning the chaplain on the "Bombay" came on board and presented Mrs. TROOP with a beautiful fan, as a token of esteem. (see original for letters of thanks from Capt. Colin A. CAMPBELL, R.N., late H.M.S. "Bombay" and Charles R. ELLIOTT, Rear Admiral as well as burning of the ship)