Bicycles and strategy? say no more!
Just take a page from real life and introduce the mechanic of... DOPING!!!
Dope your player so much that he can perform at peak power but not so much that he will die of cardiac arrest! the trill! the risk!
But seriously, a tactic cycling game sounds very weird, i can think of this: the scenario is divided in squared areas, or rectangles since its a race, and every area has a percentage of risk and a percentage of speed, meaning that the most risking areas can provide speed boosts but you risk the bicycle getting damaged, the player has to choose a route with minimizes the risk but maximizes the speed, and if several cyclists happen to be in the same area at the same time their speed decreases but the risk is the same
The other side of the strategy would be to buy stronger but slower parts for the bicycle or weaker but faster parts, this would allow to traverse areas with a certain level of risk with no risk at all obtaining a boost from the area even if the bicycle is slower, then the real strategy would come from selecting the area less likely to be occuppied by other players to avoid the speed penalty