It's worth noting that most people nowadays don't buy bonds directly, you would normally hold them through an ETF/index fund like BND or TLT. Yields typically drop when there's a flight to quality (i.e., people selling stocks to buy bonds). The upward pressure on bond prices drives yields down because people are willing to pay more for lower yields. Bonds are almost like a future of expected return on capital. If bond prices are high and yields are low, it suggests the market thinks equities will have a lower return.

Bonds and stocks have been fairly non-correlated over recent years, but this hasn't always been so. It's great for modern portfolio theory (i.e., holding a portion of stocks and bonds and rebalancing periodically). There's no guarantee that it will stay this way.

Anyway, I'm not giving investment advice, but I think the current market panic is short term and non-systemic, so it's not a terrible idea to consider rebalancing from bonds into stocks while the prices are good. If you think the market might keep dropping, then perhaps wait a little longer.

The truth is that trying to time the market is like throwing a dart at a board blindfolded, so you might as well take advantage of the current state instead of speculating about the future.