When bond prices fall, people will want to buy more bonds. This means that they will not want to hold so much money in cash or checkable deposits. This means that the quantity demanded of money goes down.
The reason for this is that falling bond prices mean that interest rates are going up. If interest rates are going up, that means that wealth held in interest bearing things like bonds will earn more than it would if interest rates were low. This means that the opportunity cost of holding money would be high when interest rates are high.