A Multi-Agent Path Finding (MAPF) problem involves multiple agents who want to reach their destinations without obstructing other agents. Although a MAPF problem needs to be solved for many real-world deployments, solving such a problem optimally is NP-hard. Many approaches have been proposed in the literature that offers sub-optimal solutions to this problem. For example, the Enhanced Conflict Based Search (ECBS) algorithm compromises the solution quality up to a constant factor to gain a notable runtime improvement. However, these algorithms use a fixed global sub-optimal bound for all agents, regardless of their preferences. In effect, with the increase in the number of agents, the runtime performance degrades. Against this backdrop, with the intent to further speed up the runtime, we propose an adaptive agent-specific sub-optimal bounding approach, called ASB-ECBS, that can be executed statically or dynamically. Specifically, ASB-ECBS can assign sub-optimal bound considering an individual agent's requirement. Additionally, we theoretically prove that the solution cost of ASB-ECBS remains within the sub-optimal bound. Finally, our extensive empirical results depict a notable improvement in the runtime by using ASB-ECBS while reducing the search space compared to the state-of-the-art MAPF algorithms.