Collaborative navigation of heterogeneous robots in unknown environments poses significant challenges due to sensing, communication, and computational limitations. In this work, a lead robot navigates toward a target while a mobile sensor robot (e.g., a drone) assists by transmitting information about its locally observed map under bandwidth constraints. We propose a framework that enables the sensor to jointly select its transmitted map points and navigation actions online, while also predicting unexplored regions of the environment. To this end, we present $β$-Sparse Gaussian Processes, a robust variational sparse Gaussian Process model for task-aware inducing point selection under cardinality constraints. Furthermore, we develop an action-selection strategy that balances task relevance with exploration. Simulations on Mars and Earth maps show that the framework can reduce path cost by 18% relative to no communication and decrease transmitted information by 76% compared to raw-data transmission baselines.