Many large-scale applications in science and business domains require the transfer of big data over high-performance networks for remote operations. Such big data transfer is increasingly supported by bandwidth reservation services that discover feasible and efficient routing options in dynamic network environments with time-varying resources. By exploring the flexility and capacity of variable paths, we formulate a generic problem of Bandwidth Scheduling with Two Variable Node-Disjoint Paths (BS-2VNDP), in which, we further consider two variable paths of fixed or variable bandwidth with negligible or non-negligible switching delay, referred to as 2VPFB/VB-0/1. We show the NP-completeness and propose a heuristic approach for each of them. We implement and test these proposed scheduling algorithms in both simulated and real-life networks. Extensive results show that they significantly outperform greedy scheduling methods in large-scale networks.