This paper presents hybrid Minimum Mean Squared Error-based estimators for wireless sensor networks with time-varying communication-bandwidth constraints, focusing on the particular application of multi-robot Cooperative Localization. When sensor nodes (e.g., robots) communicate only a quantized version of their analog measurements to the team, our proposed hybrid filters enable robots to process all available information, i.e., local analog measurements (recorded by its own sensors) as well as remote quantized measurements (collected and communicated by other sensors). Moreover, these filters are resource-aware and can utilize additional bandwidth, whenever available, to maximize estimation accuracy. Specifically, in this paper, we present two filters, the Hybrid Batch-Quantized Kalman filter (H-BQKF) and the Hybrid Iteratively-Quantized Kalman filter (H-IQKF), that can process local analog measurements along with remote measurements quantized to any number of bits. We test our proposed filters in simulations and experimentally, and demonstrate that they achieve performance comparable to the standard Kalman filter.