Neural radiance fields (NeRFs) and 3D Gaussian Splatting (3DGS) encode a scene with complementary inductive biases, but existing cross-representation distillation typically fixes one representation as teacher for the entire scene. A globally fixed teacher can propagate local reconstruction errors. We present RouteBridge, a bidirectional framework that selects the teaching direction for each ray. Its reliability estimator combines photometric residuals with representation-specific geometric evidence and routes supervision from NeRF to 3DGS, from 3DGS to NeRF, or abstains. A renderer-independent interface transfers color, opacity, and normalized depth without shared features or point correspondence. On mip-NeRF 360, the NeRF and 3DGS exports reach 28.56 and 28.77 dB, respectively. The 3DGS export improves over 3DGS by 1.56 dB and over NeRF-GS by 0.45 dB while reducing LPIPS to 0.207. On static three-view DTU, RouteBridge obtains 21.12 dB. Ablations show that both adaptive routing and geometric ray targets contribute to the improvement.