With the rapid aging of the global population, constipation has become a major gastrointestinal concern among elderly individuals. Bowel sounds provide a non-invasive acoustic signal for assessing gastrointestinal function, but their automatic analysis remains challenging due to sparsity and non-stationarity. This study proposes a two-stage bowel sound analysis framework based on continuous abdominal recordings. First, a Convolutional Neural Network-MAMBA (CNN-MAMBA) model was used for salient bowel sound detection. Second, a patient-level constipation classification model was developed using multi-view spectral representations and a Convolutional Neural Network-Conformer-Multiple Instance Learning (CNN-Conformer-MIL) architecture. On a held-out test set, the detection model achieved an accuracy of 0.87, an F1-score of 0.78, and a ROC-AUC of 0.93. For patient-level classification under binary Bristol Stool Form Scale (BSFS) grouping, five-fold cross-validation yielded a mean accuracy of 0.665 and an F1-score of 0.755. All BSFS labels were annotated by clinical physicians and temporally aligned with bowel sound recording. Given the modest improvement and cross-validation variability, the patient-level results should be interpreted as preliminary feasibility evidence. These findings suggest that bowel sound analysis may serve as an auxiliary screening or longitudinal monitoring tool rather than a stand-alone diagnostic system.