Scaling superconducting quantum processors requires interconnects that provide both non-local connectivity and parallel entangling operations. Nearest-neighbour couplings require distant interactions to be routed through SWAP networks, increasing the native two-qubit-gate count and potentially extending the circuit critical path. Here we introduce a bus-based reconfigurable quantum router for modular superconducting processors. Flux-tunable SQUID couplers selectively connect interface qubits to two shared buses, allowing destructive interference to suppress idle interactions while supporting two disjoint controlled-Z (CZ) gates in parallel. Full-system Hamiltonian simulations yield parallel-gate errors at the level of 10⁻³, and open-system analysis identifies the coherence requirements for high-fidelity operation. We further assess the circuit-level consequences using hardware-aware compilation and resource-constrained scheduling. For 36-qubit quantum Fourier transform (QFT), QAOA-MaxCut and random-pairing circuits, the router reduces the median SWAP count by up to 34% and the native CZ count by up to 20% relative to a matched two-dimensional grid. End-to-end depth reduction is circuit dependent, reaching 20% for QAOA-MaxCut but remaining negligible for the QFT despite its lower gate count. These results show that enhanced connectivity and schedulable parallelism provide distinct benefits, establishing the router as a compiler-visible hardware resource for modular superconducting quantum processors.