We demonstrate conditional entanglement swapping, i.e. teleportation of entanglement, between time-bin qubits at the telecommunication wavelength of 1536.4 nm with high fidelity of 87%. Our system is deployable, utilizing modular, off-the-shelf, fiber-coupled, and electrically controlled components such as electro-optic modulators. It leverages the precise timing resolution of superconducting nanowire detectors, which are controlled and read out via a custom developed graphical user interface. The swapping process is described, interpreted, and guided using characteristic function-based analytical modeling that accounts for realistic imperfections. Our system supports quantum networking protocols, including source-independent quantum key distribution, with an estimated secret key rate of approximately 0.5 bits per sifted bit.