All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Since you are not sure that the bin became impure with dogs’ saliva, then your clothes do not become impure by touching the bin because in principle it (the bin) is pure. This principle is not removed by doubt. Also, if you are sure that the bin is impure, and the impurity is dry and your clothes are dry, then the impurity is not transferred to your clothes by touching the bin.
But if your clothes or your hand is wet and it touches the impurity, then it becomes impure and purifying it will be by washing it seven times one of which must be with soil or soap in case of the impurity of dog. Indeed, we have issued Fatwa 90907 clarifying that in principle things are pure and that a Muslim should not open a door for whispers to bother him. We have also issued Fataawa 91541 and 83729 clarifying that wet impurity transfers from an item to another. Also, Fatwa 81546 clarifies that the impurity is not transferred from a dry impure item to another item that is dry.
As regards whether or not the impurity is removed by rain water, then if the impurity is on the ground, it becomes pure with the water of the rain even if it is the impurity of dog. If the rain that falls on the ground is more than the impurity by which it is contaminated, then the ground becomes pure with that rain. That is because if the water is more than the impurity which contaminates the ground, then the ground becomes pure; the evidence about this is the Hadeeth about the Bedouin who urinated in the mosque.
However, if the impurity is on the clothes or the hand, and the like, then it must be washed seven times one of which must be with soil as in this case these things do not become pure with the rain water.
Allaah Knows best.