In traditional IP networks, border gateway protocol (BGP) serves as the dominant protocol for inter-domain routing information exchange. In a hybrid network with both traditional network domains and software-defined networking (SDN) domains, the simultaneous inter-domain routing information exchange requires collaboration among different autonomous systems (ASes). However, the rigid routing policies of the conventional BGP are sometimes inadequate to meet the demand of applications with low-latency requirements like augmented reality (AR). In this paper, we propose a Latency Reduction Software-Defined BGP (LRSD-BGP) framework to reduce the latency in inter-domain initial link setup. Furthermore, a controller-to-controller (C2C) communication module is designed to accelerate the routing link establishment procedure of inter-domain traffic by pre-allocating and installing routing paths for the AS in the next hop. LRSD-BGP is evaluated in terms of BGP convergence time and first round-trip time (RTT). Experimental results demonstrated that LRSD-BGP can outperform SD-BGP in terms of first RTT even in highly loaded cases.