Parameterised configurations for FPGAs are configuration bitstreams of which some of the bits are defined as Boolean functions of parameters. By evaluating these Boolean functions using different parameter values, it is possible to quickly and efficiently derive specialised configuration bitstreams with different properties. Generating and using parameterized configurations requires a new tool flow. In this paper we propose a novel algorithm for the routing step of this tool flow. This new router, called the connection bundle router, is able to route a circuit with parameterized interconnections. It produces routing solutions in less time (up to a factor 5,2) and with a better quality in terms of number of wires (up to 38%) and minimum track width (up to 25%) than its predecessors. The connection bundle router is fully automated and uses a scalable connection-based representation for the parameterized interconnections in a tunable circuit.