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I was looking at the historical prices of iShares Core U.S. Aggregate Bond ETF (AGG), and Vanguard Short-Term Inflation-Protected Securities ETF (VTIP):

iShares Core U.S. Aggregate Bond ETF (AGG) Vanguard Short-Term Inflation-Protected Securities ETF (VTIP)

What explains the sudden dip in bond prices (aka sudden spike in yields) in March 2020, and the equally sudden recovery of bond prices (aka sudden decline in yields)?

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Normally, when the market is tanking, investors and traders move into bonds for safety. In early March, US and German 10 year securities hit new short term highs as the stock market drop began. When equity selling accelerated, routing stock markets, bond selling took hold as investors and traders needed to raise cash.

Another factor was that large corporations needed cash for ongoing operations and were drawing on their credit lines. In order to meet this demand, US banks sold Treasuries to meet the demand. When the Fed entered the market to shore up the system, bonds rallied.

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    Yes, it was a temporary liquidity event where nearly all assets were sold for cash. Even money market funds lost a stunning 4%. The Fed and governments worldwide responded with massive liquidity injections that dwarf even the 2008 crisis.
    – Keith Knauber
    Jun 14, 2020 at 6:25
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The most likely explanation is margin calls and the Fed:

“The concomitant sell-off in both the risk-free asset, bunds, as well as in credit and equities can either mean that markets are pricing in unrealistic bond-supply shocks and/or, more likely, mean that markets are de-leveraging,” wrote Erjon Satko, a strategist at Bank of America Merrill Lynch. “Times are exceptional.”

Leveraged investors often see margin calls as volatility spikes and can be forced to sell liquid securities, including bond futures, as a result. The change in positions across German, French, Italian, U.S. and Japanese bond futures suggests an enormous de-leveraging has taken place.

https://www.bloomberg.com/news/articles/2020-03-19/enormous-de-leveraging-in-bond-market-smacks-of-margin-call-rush

The Fed pledged to buy as much government-backed debt as needed to bolster the markets for housing and Treasury bonds. It announced that it would buy corporate bonds, including the riskiest investment-grade debt, for the first time in its history. And it promised to unveil more, including supports for small businesses, in the days and weeks to come.

https://www.nytimes.com/2020/03/23/business/economy/coronavirus-fed-bond-buying.html

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