Drug resistance to chemotherapeutic agents remains a formidable challenge in cancer treatment, significantly impacting treatment efficacy. Extensive research has exposed the intimate involvement of noncoding RNAs (ncRNAs) in conferring resistance to cancer drugs. Understanding the intricate associations between ncRNAs and drug resistance is of pivotal importance in advancing clinical interventions and expediting drug development. However, traditional biological experimental methods are hampered by limitations, such as labor intensiveness, time consumption, and constraints in scalability. Addressing these challenges necessitates the development of efficient computational methods for the accurate prediction of potential ncRNA-drug resistance associations (NDRA). However, most existing predictive models primarily focus on known ncRNA-drug resistance associations, often neglecting the critical aspect of similarity information between ncRNAs and drug resistance. This oversight may hinder the accuracy of characterizing these associations. To overcome the limitations of existing computational models, we proposed B-NDRA, a computational framework designed for the discovery of drug resistance-related ncRNA. Initially, we constructed a heterogeneous graph that integrates ncRNA-drug resistance pairs, leveraging both known associations and similarity fusion information between ncRNAs and drug resistance. Subsequently, we employed an attention mechanism to aggregate local features of graph nodes following a dimensionality reduction of node features. Further, a graph neural network (GNN) facilitated the learning of global node embeddings. Notably, the integration of dual adaptive deep adjustment architectures, encompassing intrablock and interblock methodologies, enabled efficient extraction of global features while balancing local and global features. Finally, B-NDRA employed a multilayer perceptron to predict associations between ncRNAs and drug resistance. Through rigorous 5-fold cross-validation, B-NDRA achieved average AUC, AUPR, Accuracy, Precision, Recall, and F1-score values of 92.2%, 91.9%, 84.88%, 86.9%, 82.37%, and 84.44%, respectively. Furthermore, comparative evaluations were conducted on established models, namely, GAEMDA, GRPAMDA, and LRGCPND. The results, obtained through three distinct 5-fold cross-validation strategies, demonstrated a notable performance improvement across almost all metrics for our B-NDRA. Specific case studies targeting Doxorubicin and Imatinib further validated the practicality of our B-NDRA in discovering potential NDRA. These results confirm the potential of our B-NDRA as a valuable tool in advancing cancer research and therapeutic development. The source code and data set of B-NDRA can be found at https://github.com/XuanLi1145/B-NDRA.