Bogue was the youngest son of John Bogue, M.D., of Fareham, Hampshire, and was born at Titchfield, Hampshire on 24 October 1782. He entered the Royal Military Academy, Woolwich as a cadet on 31 January 1797, passing out as a second lieutenant of the Royal Artillery on 14 July 1798. He was then promoted to the rank of Lieutenant on 10 February 1800 and became a second captain on 18 March 1806. He was appointed to 'A' Troop Royal Horse Artillery in 1803, and transferred to 'B' Troop in 1804. 'B' Troop was sent to Spain in 1808, reaching Corunna on 9 November. This was the period of General Sir John Moore’s advance into Spain to confront Napoleon. 'B' Troop were present at the successful cavalry actions at Sahagún and Benavente, besides taking part in the Battle of Corunna.
Following the disappointing experimental field trials of Congreve rockets in 1807 and 1810, the first commitment by the Royal Artillery to the use of rockets was in September 1811. The Board of Ordnance placed a detachment of thirty-two men of the Royal Horse Artillery, under Second Captain Richard Bogue, at Congreve's disposal for further integrating rockets into the artillery. This detachment experimented with the weapon both at Woolwich and at Bagshot, helping Congreve refine his system for eventual use by horse artillery. On 7 June 1813 came orders designating Bogue's unit the "Rocket Brigade" and recommending that it be brought up to full strength and tried in actual service. The Rocket Brigade landed at Wismar, in northern Germany, on 8 August and Bogue marched to join the Army of the North commanded by Crown Prince John of Sweden.
How the Rocket Brigade was brought into action on the third day of the Battle of Leipzig on 18 October 1813 is described in a letter which Lieutenant John Jones, aide-de-camp to Sir Charles Stewart, wrote to Captain Bogue’s father-in-law John Hanson.
At the commencement of the action on the morning of the 18th, Captain Bogue addressed himself to General Wintzingerode, commanding the advance of the Crown Prince, expressing his desire to see the enemy, and requesting permission to engage. The General, much struck with the gallantry and spirit of the address, granted as a guard a squadron of dragoons, and requested Captain Bogue to follow his own plans and judgement.
Captain Bogue lost no time in advancing to the attack of the village of Paunsdorf, then in possession of five of the enemy’s battalions, upon whom he opened, in advance of the whole army a most destructive fire. This was returned by musketry, and for some time a very hot combat ensured, when the enemy, unable to withstand the well directed fire of Captain Bogue’s brigade, fell into confusion and began to retreat. Captain Bogue, seizing the moment, charged at the head of the squadron of cavalry, and enemy, terrified at his approach, turned round, and taking off their caps, gave three huzzas, and every man, to the number of between two and three thousand, surrendered to the Rocket Brigade, which, I believe, did not exceed 200 men.
The intelligence of this success being communicated to the Crown Prince, he sent his thanks to Captain Bogue for such eminent services, requesting at the same time that he would continue his exertions; and the brigade proceeded in consequence to the attack of (I believe) the village of Sommerfeld [should be Sellerhausen] still further in advance. Sir C. Stewart accompanied the brigade and I was of the party. The situation taken up on the flank of the village was exposed to a most heavy fire, both of cannon-balls and grapeshot from the enemy’s line, and from the riflemen [musket-armed skirmishers] in the village. A ball from the latter soon deprived us of the exertions of poor Bogue; it entered below the eye and passing through the head caused instantaneous death.
Richard Bogue was buried in Taucha churchyard, four miles away from where he fell, and a stone monument was erected over his grave in 1815 by national subscription. This monument was restored in 1896, and again in 1930. In Tichfield church a commemorative plaque in his memory was placed in the choir, near the altar. In later years, the village of Taucha named a street in his memory. In January 1814, the Crown Prince of Sweden sent the Swedish Military Order of the Sword, 4th Class (Knight) to Captain Bogue's widow and also a gift of 10,000 dollars.