Discriminating early-stage nasopharyngeal carcinoma (NPC) from benign hyperplasia (BH) on MRI is a challenging but important task for the early detection of NPC in screening programs. Radiomics models have the potential to meet this challenge, but instability in the feature selection step may reduce their reliability. Therefore, in this study, we aim to discriminate between early-stage T1 NPC and BH on MRI using radiomics and propose a method to improve the stability of the feature selection step in the radiomics pipeline. A radiomics model was trained using data from 442 patients (221 early-stage T1 NPC and 221 with BH) scanned at 3T and tested on 213 patients (99 early-stage T1 NPC and 114 BH) scanned at 1.5T. To verify the improvement in feature selection stability, we compared our proposed ensemble technique, which uses a combination of bagging and boosting (BB-RENT), with the well-established elastic net. The proposed radiomics model achieved an area under the curve of 0.85 (95% confidence interval (CI): 0.82–0.89) and 0.80 (95% CI: 0.74–0.86) in discriminating NPC and BH in the 3T training and 1.5T testing cohort, respectively, using 17 features selected from a pool of 422 features by the proposed feature selection technique. BB-RENT showed a better feature selection stability compared to the elastic net (Jaccard index = 0.39 ± 0.14 and 0.24 ± 0.06, respectively; p < 0.001).