Smart transportation, which is an important dimension of smart cities, includes both intelligent and 'green' transportation solutions. Cycling, as one of the most sustainable forms of transportation, is and should be an important component of smart cities. Electric bicycles, which are the most popular electric vehicles, subscribe to this type of transportation. They have several advantages when compared with traditional bicycles but have issues that relate to battery-limited capacity and long periods of charging as well. Consequently, energy-efficient solutions for electric bicycles are of very high research interest. Research on vehicular-communications-based energy-efficient solutions for electric vehicles is still in the early stages. Among electric vehicles, electric bicycles distinguish themselves as a special class as they have different characteristics and road-related requirements. This paper proposes a novel vehicular-communications-based speed advisory system for electric bicycles. The solution recommends strategic riding (i.e., the appropriate speed) when bicycles are approaching a signaled intersection to avoid high-power-consumption scenarios. The proposed approach includes a fuzzy-logic-based wind-aware speed adaptation policy, as, among all the other vehicles, bicycles are mostly affected by wind. Experimental results based on a real testbed and extensive simulation-based testing demonstrate that, by using the proposed solution, significant energy savings are recorded. In addition, an analysis on comfort-related metrics shows that the proposed solution can also contribute to improving the cycling experience.