The transit signal priority (TSP), as an effective method to address public transport operation issues, has been widely applied. With the continuous advancement of connected technology, research on developing bus priority strategies using vehicle-to-everything (V2X) technology is gaining increasing attention. However, existing studies on TSP mainly focus on exclusive bus lanes, overlooking the adverse impact of private vehicle queues at intersections on bus priority strategies. To more effectively evaluate the optimization effect of bus priority under non-bus lane conditions, this paper proposes a cooperative control method combining signal control and eco-speed guidance in a connected environment. The objective is to maximize the reduction in delays for both buses and private vehicles at intersections and optimize carbon emission reduction. Initially, an Extended Kalman Filter (EKF) is employed to predict the arrival time of buses at intersections and the signal status. Building upon this, optimal timings for phase adjustments and the best bus trajectories are calculated using signal control and eco-speed guidance models. This approach aims to enhance bus operational efficiency while further lowering traffic carbon emissions. The effectiveness of the proposed model is verified using Zhengzhou city as a case study and compared against scenarios involving NTSP, TSP, and speed guidance. The results demonstrate that, in the absence of exclusive bus lanes, the proposed method not only ensures the stability of bus operations but also achieves significant bus priority and carbon emission benefits while mitigating the adverse impact of bus priority on private vehicles to a certain extent.