WiFi densification leads to the existence of multiple overlapping coverage areas, which allows user stations (STAs) to choose between different Access Points (APs). The standard WiFi association method makes STAs select the AP with the strongest signal, which in many cases leads to underutilization of some APs while overcrowding others. To mitigate this situation, Reinforcement Learning techniques such as Multi-Armed Bandits (MABs) can be used to dynamically learn the optimal mapping between APs and STAs, and so redistribute the STAs among the available APs accordingly. This is an especially challenging problem since the network response observed by a given STA depends on the behavior of the others. Therefore, it is very difficult to predict without a global view of the network. In this paper, we focus on solving this problem in a decentralized way, where STAs independently explore the different APs inside their coverage range, and select the one that better satisfy their needs. To do it, we propose a novel approach called Opportunistic epsilon-greedy with Stickiness that halts the exploration when a suitable AP is found, only resuming the exploration after several unsatisfactory association rounds. With this approach, we reduce significantly the network response dynamics, improving the ability of the STAs to find a solution faster, as well as achieving a more efficient use of the network resources. We show that to use MABs efficiently in the considered scenario, we need to keep the exploration rate of the STAs low, as a high exploration rate leads to high variability in the network, preventing the STAs from properly learning. Moreover, we investigate how the characteristics of the scenario (position of the APs and STAs, mobility of the STAs, traffic loads, and channel allocation strategies) impact on the learning process, as well as on the achievable system performance. We also show that all STAs in the network improve their performance even when only a few STAs participate in the search for a better AP (i.e., implement the proposed solution). We study a case where stations arrive progressively to the system, showing that the considered approach is also suitable in such a non-stationary set-up. Finally, we compare our MABs-based approach to a load-aware AP selection mechanism, which serves us to illustrate the potential gains and drawbacks of using MABs.