The recent surge in the attention garnered by blockchain technology, an immutable ledger enabling decentralized transactions, is noteworthy. However, the security of blockchain remains susceptible to various attacks, including distributed denial-of-service (DDoS) attacks, which have increasingly targeted Bitcoin services. In response, deep learning algorithms have emerged as a potent solution to complex problems within the realm of information science. This study proposes a novel approach, utilizing these algorithms within hybrid frameworks, to address intricate cybersecurity issues. The methodologies were implemented and fine-tuned within a Python environment. Initially, a technique known as data augmentation was applied to an experimental domain aimed at verifying efficiency and boosting precision in complex datasets. Data augmentation, a method of generating new data points from existing ones, artificially enhances the volume of data. A Conditional Table Generative Adversarial Network (CTGAN) approach was adopted for the creation of tabular synthetic data. The utilization of synthetic data was found to enhance the model's performance and robustness compared to the exclusive use of original data. Subsequently, a binary classification hybrid deep learning model, incorporating Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) algorithms, was proposed for the detection of DDoS attacks within cryptocurrency networks. The proposed model was then validated using actual instances of DDoS attacks within the Bitcoin service dataset. The validation process incorporated a test set comprising 20% of the augmented data. Evidently, the proposed model outperformed standard deep learning implementations, achieving an impressive accuracy of approximately 95.84%. This study, therefore, presents a promising approach to mitigating DDoS attacks within the Bitcoin ecosystem.