This study investigates the impact of social media sentiment on Bitcoin (BTC) price volatility by using various deep learning models. Sentiment scores were calculated from more than 60,000 Reddit and Twitter posts using CryptoBERT, and then combined with the corresponding BTC market data to form a comprehensive time-series dataset. Further, feature engineering techniques including volatility, momentum, lagged sentiment scores, and rolling averages were then applied to capture temporal dependencies in the respective datasets, and various deep learning models namely Long Short-Term Memory (LSTM), Attention-Enhanced LSTM, Gated Recurrent Unit (GRU), and a Hybrid LSTM-XGBoost model were then evaluated on metrics like Mean Squared Error (MSE), Mean Absolute Error (MAE), R2 score and Directional Accuracy. The results show decent sentiment-market correlations, with Attention-based models achieving up to 74% directional accuracy. These findings highlight the potential of sentiment-aware models in enhancing short-term cryptocurrency volatility prediction.