Bicycling is an under-rated skill in most people's campaigns because now bicycles are now just seen as leisure items, or for commuting to work in a city.
During the first half of the 20th century, they were more significant, particularly in warfare. When a war was being fought in an environment with good roads - the First and Second World Wars in Europe as well as the Spanish civil war and various internecine fights in the Balkans - bicycles represented a resource which could move troops quickly and easily. Bicycle-mounted troops could travel more than twice as fast as those on foot, and with considerably less effort and wear on boot-leather. Troops travelled quickly and arrived relatively fresh at the battlefield.
Effectively, the bicycle-mounted infantry were the hobilars (mounted infantry) or mounted archers of the twentieth century - except that their mounts needed no fodder, didn't need horse-holders when the troops dismounted and went into action, and could be shipped by the hundreds in a single railcar.
Even as late as the Vietnam War, bicycles performed a major role in warfare. For most of its length, the Ho Chi Min Trail was basically a series of interconnected footpaths running over and through terrain that a larger road could not have handled. This dispersed nature made the trail very difficult for the Americans to disrupt/destroy even with their massive technological advantages.
The couriers carrying stuff along the Trail loaded it up on bicycles. Each bike would be loaded with up to 200lb of cargo (weapons, ammo and food), far more than a man could carry, but within the capability of a man pushing a wheeled vehicle. It was a transport system that needed no fuel depots or fuel distribution networks, most repairs to broken-down bikes could be done by the courier and even major problems could be fixed in any village workshop - and of course the civilians were using bikes too, so those facilities were always available and were not seen as resources for war.
Player-characters operating in cities where the bicycle is common should always have the skill. Think how many movies you have seen where the hero is desperate to get across the city, only to find his taxi stuck in traffic. ("Go across the park. No, not on the road, through the park!") Adventurers in that position can easily leap out of the cab, shove a commuter off his bike, and take off, crossing the city at 10-15 mph regardless of traffic conditions.