The Bible doesn't promise that everything will be rosey here on this earth. The promise of everything being rosey is in the kingdom of heaven.
Why does God allow bad things to happen? God even says in his word that he allows to rain to fall on the just and unjust. Do not "bad things" often bring a lesson? If you have children you should understand this. You try and tell your child this is a bad idea to do that but yet they go ahead and learn the hard way. Thats why we call God our Heavenly Father. He has done the same thing with us, He has told us in His word, right and wrong, yet we as disobedient children do it our own way.
Yes there is suffering in the world, by both Christain and nonchristian. Why would a Loving God allow this? Read the book of Job. It explains it very well. Jesus Himself suffered on the Cross. He was beaten, spit upon, had a crown of thorns forced on his head. He had nails in His hands and feet. Yet through this pain and suffering He willing gave Himself a sacracifice for anyone that would believe eternal life.
I may die from anything, cancer, murder, car wreck, or some other way. It will not effect my faith in God because it happens to me. Because I understand that this life is nothing but a trial. I have a better home awaiting!