Accurate estimation of the wetting distribution pattern (WDP) around the emitters of a drip irrigation system in sloping lands can minimize surface runoff losses by determining the placement status of plants and emitters. In this study, both experimental and computational efforts were made to estimate the WDP in sloping lands with drip irrigation. 486 sets of laboratory experiments were conducted and a series of soil characteristics data were collected. Particularly, the upstream wetting radius (R-), downstream wetting radius (R+), and wetting depth (D) were measured and further used as the target variables of three modeling scenarios. In the modeling effort, a new hybrid framework, consisting of a light gradient boosting machine (LightGBM) and best subset regression (BSR) integrated with bidirectional recurrent neural network (Bi-RNN), was developed for precise simulation of WDP. The main model (i.e., Bi-RNN) was compared with the Elman recurrent neural network (ERNN) and bagging regression tree (BGRT) in the advanced multi-filtering framework for all the scenarios. In the first stage, the LightGBM tree-based feature selection filtered the significant predictors in each scenario. In the second stage, the best possible three input combinations using the selected N predictors in the first stage were extracted among 2N possible combinations via the BSR strategy. The performances of the models were evaluated by using different statistical metrics. It was demonstrated that Bi-RNN achieved the highest accuracy in all the hybrid models for the three scenarios, followed by the ERRN and BGRT models. Also, a resampling bootstrap-based uncertainty analysis proved that the developed multistage-filtering strategy before the deep learning model feeding decreased the uncertainty associated with input combination effects. By determining the placement status of plants and emitters, the proposed framework can effectively reduce surface runoff losses.