Yikes, sounds like a mess. You have a couple of things going on. The white spots on the leaves are probably Powdery Mildew, a fungal disease that occurs during humid weather. If you are spray watering your roses, stop. Every time you wet the leaves, you are inviting Powdery Mildew, Black Spot and other fungal diseases that can afflict roses. Water the soil below the plants (not just your roses but all you landscape plants, flowers and vegetables) More on that HERE.
Now that the disease is established, you’ll need to treat it with a strong fungicide like Infuse following the directions on the label. You can find Infuse at Hewitts.
Your “cotton liking stuff” is a soft scale insect. It is sucking nutrients from the rose. Between that and the mildew, the rose is so weak that it is aboprting the flowerbuds in a n effort to conserve enough energy to simply survive. To kill the scale, you’ll need to spray with Bonide Rose Rx following the direction s on the label…it will take multiple spraying to get the scale under control.
In the future, you should consider spraying with Rose RX earlier in the season before the pests show up to prevent these issues. Above all, DON’T spray water your plants.