Mobile Crowdsensing (MCS) represents a transformative approach to collecting data from the environment as it utilizes the ubiquity and sensory capabilities of mobile devices with human participants. This paradigm enables scales of data collection critical for applications ranging from environmental monitoring to urban planning. However, the effective harnessing of this distributed data collection capability faces significant challenges. One of the most significant challenges is the variability in the sensing qualities of the participating devices while they are initially unknown and must be learned over time to optimize task assignments. This paper tackles the dual challenges of managing task diversity to mitigate data redundancy and optimizing task assignment amidst the inherent variability of worker performance. We introduce a novel model that dynamically adjusts task weights based on assignment frequency to promote diversity and incorporates a flexible approach to account for the different qualities of task completion, especially in scenarios with overlapping task assignments. Our strategy aims to maximize the overall weighted quality of data collected within the constraints of a predefined budget. Our strategy leverages a combinatorial multi-armed bandit framework with an upper confidence bound approach to guide decision-making. We demonstrate the efficacy of our approach through a combination of regret analysis and simulations grounded in realistic scenarios.