This study investigates the potential of utilizing nonparametric, nonlinear machine learning (ML) algorithms, in conjunction with vegetation indices (VIs) derived from unmanned aerial vehicles (UAVs), to estimate the height-to-node ratio and the fourth internode length in cotton plants. The objective was to enhance the monitoring of these traits, thereby providing more accurate guidance on the optimal timing of plant growth regulator (PGR) applications. Data was collected from eight plots in our experimental field, with six plots used for model training and two for testing. During model development, the performance was assessed using nested 5-fold cross-validation, repeated three times with different partitions. For each algorithm, hyperparameters were tuned on the inner folds via Bayesian optimization with a Gaussian process surrogate, and the tuned model was evaluated on the corresponding outer test fold. We evaluated the performance of the ML algorithms using the Friedman test and interpreted their result using the Wilcoxon signed-rank test. The results demonstrate that VIs, combined with ML algorithms, can reliably estimate both the height-to-node ratio and the length of the fourth internode. Additionally, among the tested ML algorithms, Support Vector Regression (SVR) demonstrated superior performance for predicting height-to-node ratio, with an R² value of 0.8257 (95% CI: 0.7404 - 0.9110), RMSE value of 0.0998 (95% CI: 0.0953 - 0.1044), and rRMSE value of 5.51 (95% CI: 5.30 - 5.7). Meanwhile, the CatBoost demonstrated higher performance in estimating the fourth internode length, with an R² value of 0.799 (95% CI: 0.7570 - 0.8415), an RMSE of 0.1788 (95% CI: 0.1631 - 0.1945), and a rRMSE of 10.64 (95% CI: 9.90 - 11.38). Furthermore, using the Shapley Additive exPlanations (SHAP) approach, we revealed the contribution of each of the VI to the model's prediction. Overall, the findings demonstrate that UAV-derived VIs, combined with a machine learning algorithm, can consistently estimate these cotton traits. Additionally, this approach can replace traditional field-based measurements, thereby supporting more efficient monitoring and precise PGR management decisions.