Even worse...let's say interest rates do not go up....but a lot of people sell their holdings in their bond fund (e.g. to "buy the dip" or "to have more cash at the bank" or "to buy some food" or "to buy guns and ammo" or ...). The bond fund MUST sell those bonds to make up for redemption. However, since the market is in free fall: A lot of the folks (institutions) who might have bid for the bond are no longer providing a bid, or people are widening their spread (what they will bid to buy vs what they ask to sell) due to the increased risk and volatility.
So even if the underlying companies don't have increased risk of default (which unfortunately they do), the bonds go down due to the increased risk spread.
It is just the way it is in frantic times.
The best thing that could happen is that the market settles down. No down crazy, no up crazy. Time is needed for proper analysis and price discovery, and things have been happening so fast that it is impossible to keep up.
One more thought - the virus is now rampaging through lower New York and Long Island. This is the very same area where a lot of the traders (both equity and bonds) live. So on top of the financial craziness they are also living through and fearful of what will happen to them personally. This too makes the market less efficient and prone to wild swings. Will a person, given the craziness, take on more risk? What are the risk departments doing?
ETA: I'm not saying there aren't possibly good buys here - in reality I have no idea, and it is times of craziness where you might find the really good buys.