The inherent mobility characterizing users in fog computing environments along with the limited wireless range of their serving fog nodes (FNs) drives the need for designing efficient mobility management (MM) mechanisms. This ensures that users' resource-intensive tasks are always served by the most suitable FNs in their vicinity. However, since MM decisionmaking requires control information which is difficult to predict accurately a-priori, such as the users' mobility patterns and the dynamics of the FNs, researchers have started to shift their attention towards MM solutions based on online learning. Motivated by this approach, in this paper, we consider a bandit learning model to address the mobility-induced FN selection problem, with a particular focus on scenarios with a high FN density. Following this approach, a software agent implemented within the user's device learns the FNs' delay performances via trial and error, by sending them the user's computation tasks and observing the perceived delay, with the goal of minimizing the accumulated delay. This task is particularly challenging when considering a high FN density, since the number of unknown FNs that need to be explored is high, while the time that can be spent on learning their performances is limited, given the user's mobility. Therefore, to address this issue, we propose to limit the number of explorations to a small subset of the FNs. As a result, the user can still have time to be served by the FN that was found to yield the lowest delay performance. Using real world mobility traces and task generation patterns, we found that it pays off to limit the number of explorations in high FN density scenarios. This is shown through significant improvements in the cumulative regret as well as the instantaneous delay, compared to the case where all newly-appeared FNs are explored.