Chest computed tomography (CT) based analysis and diagnosis of the Coronavirus Disease 2019 (COVID-19) plays a key role in combating the outbreak of the pandemic that has rapidly spread worldwide. To date, the disease has infected more than 18 million people with over 690k deaths reported. Reverse transcription polymerase chain reaction (RT-PCR) is the current gold standard for clinical diagnosis but may produce false positives; thus, chest CT based diagnosis is considered more viable. However, accurate screening is challenging due to difficulty in annotation efforts of infected areas, curation of large datasets, and the slight discrepancies between COVID-19 and other viral pneumonia. In this study, we propose an attention-based end-to-end weakly supervised framework for the rapid diagnosis of COVID-19 and bacterial pneumonia based on multiple instance learning (MIL). We further incorporate unsupervised contrastive learning for improved accuracy with attention applied both in spatial and latent contexts, herein we propose Dual Attention Contrastive based MIL (DA-CMIL). DA-CMIL takes as input a several patient CT slices (considered as a bag of instances) and outputs a single label. Attention based pooling is applied to implicitly select key slices in latent space, and spatial attention learns slice spatial context for interpretable diagnosis. A contrastive loss is applied at the instance level to encode similarity in features from the same patient against pooled patient features. Empirical results show our algorithm achieves an overall accuracy of 98.6% and an AUC of 98.4%. Moreover, ablation studies show the benefit of contrastive learning with MIL.