You can generally boil the suspect list down to two types of white spiders if you see them on your roses: crab spiders and spider mites. One looks to hideout on the blossom itself and the other just looks as flowers as a "rest area" on their way to the leaves. Inspect the roses and the leaves to determine who your enemy is and treat the plant and white spiders accordingly to eradicate them from your rose plant.
The white crab spider has tiny legs and the capability to walk sideways -- just like a crab, and hence its name. They are also called flower spiders. Crab spiders are a bigger problem for other insects than they actually are for your roses. These spiders nestle themselves inside the flower to stake out and snare bees and leafhoppers. When viewed from this perspective, the crab spider is actually more of a friend than a foe. The crab spider will serve as a beneficial predator, ridding the roses of leafhoppers, who will chew away at the leaves of the rose plant.
Spider mites pose the most danger, in terms of damage to roses. Three types of spider mites typically invade rose plants -- the two-spotted mite, the Pacific mite and the strawberry mite. If the spider on your rose is white in color, it is more than likely a two-spotted or a Pacific spider mite. You may spot the mites inside your rose buds and blossoms, but they are actually en route to another part of the plant: the rose leaves. Once they reach the leaves, they will chomp away, start construction on webs and leave a trail and residue that can make the leaves look as if they are stippled or bleached, with tiny white or bronze-colored dots. This damage will cause the leaves to eventually turn yellow, dry up and fall off the plant stems.
One of the best courses of prevention is to keep the rose plant well watered. A dusty environment is like a "welcome" sign for spider mites. Periodic watering of leaves is also a preventive measure to make it harder for spider mites to set up a homestead on your rose plants. Also, inspect the undersides of leaves on the plant for signs of infestation such as webbing, dots or stippling on at least a weekly basis. Be vigilant about inspections during hot weather. Spider mites can reproduce rapidly if the weather is hot and the garden conditions are dry and dusty. The female can produce a whole generation of spider mite offspring in less than a week.
Crab spiders may be simply picked off of the rose with tweezers and dropped into a paper cup. This approach is safer than using insecticides, which might harm the rosebud and flowers.
To get rid of spider mites without using insecticides or chemicals, try a medium water spray. Pay attention to spraying the tops and undersides of the plant leaves, since this is where they hang out. This practice will also prevent disturbing the buds and flowers.
If you want to take a more aggressive approach, use an insecticidal soap or neem oil to treat the invasion.