This study investigates the relationship between social media sentiment and Bitcoin price volatility using advanced natural language processing techniques. We collected X data from April 10-29, 2025, analyzing cryptocurrency-related tweets alongside Bitcoin price movements obtained through the CoinGecko API. Five sentiment analysis methodologies were comparatively evaluated: VADER, TextBlob, BERTweet, RoBERTa Base, and RoBERTa Large. Bitcoin price volatility was measured using log returns to capture market fluctuations accurately. Correlation analysis revealed significant differences in methodological effectiveness. Traditional lexicon-based approaches (VADER and TextBlob) demonstrated weak correlations with volatility (r = -0.2232 and r = -0.0710 respectively). Transformer-based models showed superior performance, with RoBERTa Large achieving the strongest correlation (r = 0.4569, p = 0.0428), representing the only statistically significant relationship. The positive correlation indicates that increased social media sentiment corresponds to higher Bitcoin price volatility rather than directional price movements. These findings demonstrate that sophisticated deep learning models can effectively capture sentiment-driven market dynamics, providing valuable insights for cryptocurrency investors, trading platforms, and market analysts seeking to understand social media influence on digital asset markets.