Network slicing enables operators to efficiently support diverse applications on a common physical infrastructure. The ever-increasing densification of network deployment leads to complex and non-trivial inter-cell interference, which requires more than inaccurate analytic models to dynamically optimize resource management for network slices. In this paper, we develop a DIRP algorithm with multiple deep reinforcement learning (DRL) agents to cooperatively optimize resource partition in individual cells to fulfill the requirements of each slice, based on two alternative reward functions. Nevertheless, existing DRL approaches usually tie the pretrained model parameters to specific network environments with poor transferability, which raises practical deployment concerns in large-scale mobile networks. Hence, we design a novel transfer learning-aided DIRP (TL-DIRP) algorithm to ease the transfer of DIRP agents across different network environments in terms of sample efficiency, model reproducibility, and algorithm scalability. The TL-DIRP algorithm first centrally trains a generalized model and then transfers the "generalist" to each local agent as "specialist" with distributed finetuning and execution. TL-DIRP consists of two steps: 1) centralized training of a generalized distributed model, 2) transferring the "generalist" to each "specialist" with distributed finetuning and execution. The numerical results show that not only DIRP outperforms existing baseline approaches in terms of faster convergence and higher reward, but more importantly, TL-DIRP significantly improves the service performance, with reduced exploration cost, accelerated convergence rate, and enhanced model reproducibility. As compared to a traffic-aware baseline, TL-DIRP provides about 15% less violation ratio of the quality of service (QoS) for the worst slice service and 8.8% less violation on the average service QoS.