Faith. If God loves us, why do bad things happen? That isn't an easy answer. Some of the bad things that happen are the result of God loving us enough to give us free will. We are free to choose what we do and what we don't do. God created us with a conscience, reason, and gifts us with a whole lot of grace, so that we hopefully choose options that are in line with His will. Working counter to God's will results in actions with less than great consequences. That makes sense.
But what about those things that randomly happen. To this I would say, especially as it related to natural disasters, that the Earth has been doing what it has been doing for millions of years. Plates shift and move, air masses collide, stuff happens. People get in the way. The Earth is bigger than people. That makes sense. God has empowered people to develop ways to track storms and warn people so choices can be made.
Then the questions of illness, pain, suffering pop up. Indeed, these are the toughest because one can't reason it away. That is where faith steps in. When we struggle to understand why, our faith compels us to action. There's a reason in the suffering somewhere. It can be hard to find what the reason may be but faith leads us to it. This level of "bad" is to compel us toward God; to a dependence on Him. It doesn't make sense but it will if you have faith. It is said that hindsight is 20/20. When a person takes time to think back to a time of suffering, the fruit can be seen. What was to be learned? What was the reason? In fact, long suffering is a fruit of the Holy Spirit. How is suffering good? It brings us to dependence on God. Faith.