In recent years, Bitcoin has garnered attention as a digital currency, prompting increasing debate regarding its effects on traditional financial markets, particularly the US dollar. This study investigates the relationship between Bitcoin and the US dollar, especially in the contexts of speculative attacks, where investors attempt to devalue a currency, and short squeezes, where rapid price rises force short sellers to quickly buy back assets to avoid further losses. The study employs a novel hybrid model combining an autoregressive moving average, Generalized Autoregressive Conditional Heteroskedasticity, and Wavelet Neural Networks techniques with neural networks approaches. The results suggest that significant trading activity in Bitcoin/US dollar, particularly during speculative attacks and short squeezes, can substantially impact the US dollar/EUR market, increasing price volatility as traders adjust their strategies. These adjustments, along with risk management strategies, drive higher trading volumes and further volatility. Our findings demonstrate that our novel hybrid model combined with Quantum Recurrent Neural Networks provides the most accurate predictions, offering valuable insights to inform trading strategies in both Bitcoin/US dollar and US dollar/EUR markets. This study has important implications for policymakers and market participants, emphasising the need to understand the relationship between Bitcoin and the US dollar for financial stability and effective policy formulation. It also highlights the necessity of advanced modeling techniques to accurately predict cryptocurrency market behavior.