This paper is concerned with slicing a radio access network (RAN) for simultaneously serving two typical 5G and beyond use cases, i.e., enhanced mobile broadband (eMBB) and ultra-reliable and low latency communications (URLLC). Although many researches have been conducted to tackle this issue, few of them have considered the impact of bursty URLLC. The bursty characteristic of URLLC traffic may significantly increase the difficulty of RAN slicing on the aspect of ensuring a ultra-low packet blocking probability. To reduce the packet blocking probability, we re-visit the structure of physical resource blocks (PRBs) orchestrated for bursty URLLC traffic in the time-frequency plane based on our theoretical results. Meanwhile, we formulate the problem of slicing a RAN enabling coordinated multi-point (CoMP) transmissions for multicast eMBB and bursty URLLC service multiplexing as a multi-timescale optimization problem. The goal of this problem is to maximize multicast eMBB and bursty URLLC slice utilities, subject to physical resource constraints. To mitigate this thorny multi-timescale problem, we transform it into multiple single timescale problems by exploring the fundamental principle of a sample average approximation (SAA) technique. Next, an iterative algorithm with provable performance guarantees is developed to obtain solutions to these single timescale problems and aggregate the obtained solutions into those of the multi-timescale problem. We also design a prototype for the CoMP-enabled RAN slicing system incorporating with multicast eMBB and bursty URLLC traffic and compare the proposed iterative algorithm with the state-of-the-art algorithm to verify the effectiveness of the algorithm.