The introduction of regulated CME futures contracts on Bitcoin in 2017 raised an expectation that cryptocurrencies would become part of mainstream financial markets. This also heightened links between traditional markets and Bitcoin, implying that the cryptocurrency would be subject to systematic spillovers. This paper uses high‐frequency data to examine whether Bitcoin basis risk is linked to investor sentiment from established financial markets. Our findings indicate that extreme investor sentiment, as reflected by the tail risk in various volatility indices, including the VIX, consistently correlates with a negative Bitcoin basis, where Bitcoin futures prices are lower than spot prices. Fluctuations significantly influence this relationship in the trading volume of Bitcoin futures and are more pronounced during periods of substantial unexpected inflation and deflation. These results underline the complex dynamics between market sentiment and cryptocurrency pricing, offering insights with substantial implications for investors and policymakers.