Usually nothing so exciting. This answer will deal exclusively with the role of the British Army in peacetime during the eighteenth century. The composition and the individual careers of soldiers on campaign differed markedly from their conditions in peace. In peace time, battalions were billeted over a wide stretch of territory. For training, they performed the manual exercise in small detachments, and rarely mustering with the rest of the battalion except for annual inspections. Multi-battalion exercises were almost unknown until the American War of Independence.^1 Such an arrangement was hardly conducive to maintaining unit cohesion, and it took a significant push on the part of the regimental commanders to make a regiment 'Fit for Service'. In the mean time, soldiers could be kept busy by any number of means. The army in the 18th century was employed in lieu of a police force: Soldiers were deployed against smugglers in the West and served as a an aid to the civil power against riotous mobs, duties which the historian Alan J. Guy aptly terms "the Georgian equivalent of low intensity operations." In Ireland and Scotland, the army served as a garrison, in the latter, acting almost as an occupying force well into the 1750's.

Soldiers filled their downtime by working menial jobs, which supplemented their meager pay. In towns, these would have been jobs in the trade which the soldier had previously worked prior to enlistment, or else found seasonal agricultural employment in the country. Guy notes that "the coming of the harvest saw regiments hit by outbreaks of short-term desertion which... Were often treated with remarkable tolerance." There was a distinction Within the regiment, tailors would be employed in fitting the annual clothing issue-- though Bennet Cutbertson, a well known military author of the period, stated they should receive no extra pay for this duty. In Scotland, the army constructed roads, for which they received no extra pay. In Boston in 1770, soldiers took unskilled jobs at lower wages than those of the city's laborers, which did nothing to ingratiate the army in the eyes of the American colonists, and the practice was later forbidden.

For further reading see:

Sylvia R. Frey, The British Soldier in America: A Social History of Military Life in the Revolutionary Period

Alan J. Guy, "The Army of the Georges" in The Oxford History of the British Army

J.A. Houlding, Fit For Service: The Training of the British Army 1715-1795

^1 The Camps of Exercise at Coxheath and Warley, first held in 1778 and more or less regularly thereafter, provided a space in which the army and militia could drill and perform maneuvers in formations exceeding the battalion level.

The life of an 18th century soldier was dull and painful. Unlike soldiers now, more emphasis was placed on movement and obeying orders than straight out martial skills such as marksmanship and hand to hand combat. Think of an 18th century soldier more as a machine than a soldier, since it was ideal for them to all march the same way and fire the same way. Thus it wouldn't be possible to be a bounty hunter since they wouldn't have the necessary skills.

With that said, it was possible for soldiers to have a side job, but usually organized by their commanding officer and for the profit of the commanding officer. These jobs would usually be construction jobs (since soldiers were more machine than man, doing exactly what they were told) and got a very small portion of the pay which might be on top of the pay they were already getting from the State, if the commander was nice. Beyond that, a soldier wasn't allowed to do much or stray far from the regimental barracks during peace time.

There were mercenaries but they were more of the same, except they were for hire by their commanding officer. They would usually be paid better and better trained with the Swiss Guard of the King being the most famous group outside of the Hessians hired by the British.