Accurate link-level bicycling volume estimation is essential for sustainable urban transportation planning. However, many cities face significant challenges of high data sparsity due to limited bicycling count sensor coverage. To address this issue, we propose INSPIRE-GNN, a novel Reinforcement Learning (RL)-boosted hybrid Graph Neural Network (GNN) framework designed to optimize sensor placement and improve link-level bicycling volume estimation in data-sparse environments. INSPIRE-GNN integrates Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) with a Deep Q-Network (DQN)-based RL agent, enabling a data-driven strategic selection of sensor locations to maximize estimation performance. Applied to Melbourne's bicycling network, comprising 15,933 road segments with sensor coverage on only 141 road segments (99% sparsity) - INSPIRE-GNN demonstrates significant improvements in volume estimation by strategically selecting additional sensor locations in deployments of 50, 100, 200 and 500 sensors. Our framework outperforms traditional heuristic methods for sensor placement such as betweenness centrality, closeness centrality, observed bicycling activity and random placement, across key metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Furthermore, our experiments benchmark INSPIRE-GNN against standard machine learning and deep learning models in the bicycle volume estimation performance, underscoring its effectiveness. Our proposed framework provides transport planners actionable insights to effectively expand sensor networks, optimize sensor placement and maximize volume estimation accuracy and reliability of bicycling data for informed transportation planning decisions.