Printing so many bills will depreciate the value of dollars. This affects the value of bitcoins just the same as each bitcoins has a corresponding dollar value and when the value of the dollar drops, then the value of per bitcoin will drop as well.
I don't think that's quite the mechanism at work. It's more about the US dollar functioning as the global reserve currency during a period when investors need quick access to liquidity.
When such events occur, even safe have assets come under pressure:
Given that gold was the first safe-haven to come under pressure during this period of severe market stress, it is worth considering why this was the first to wobble (see Chart 2). We believe this is also likely due to the severity of stock market declines and the need for investors to liquidate positions and meet margin calls on risky assets (such as equities, high yield and emerging market assets).
Due to the deflationary effects of the economic shutdowns, we also probably won't feel the dollar depreciation for a while, perhaps years.