Selecting a disease-resistant rose is the single most effective way to avoid problems and the need for chemicals. You might start by considering some of the old rose varieties, many of which have natural disease resistance. You can also look to many of the modern roses, which are now being bred for improved disease resistance. Hybrid teas are notoriously disease-prone, and seem to lure every insect pest from miles around. They can be difficult to grow without an arsenal of chemical dusts and sprays.
I too, have tried the cut rose flower method, but haven't yet been successful--perhaps because there are chemical additives that the roses have soaked up, or because there are no nodes (which are the points where new shoots grow out), or because the stems have spent much of their energy producing the flowers...BUT, perhaps if the flowers were immediately cut off and some rooting hormones applied to the bottom cut ends, that may work.
Plant the rose bush seeds approximately ¼ inch deep in a seed-planting mix in seedling trays or your own planting trays. The trays need not be more than 3 to 4 inches deep for this use. When planting rose seeds from various rose bush hips, I use a separate tray for each different group of seeds and label the trays with that rose bushes name and planting date.
One way to stratify the rose seeds is to place the cleaned seeds on a paper towel (a heavyweight brand such as Bounty). Then moisten the paper towel with a solution of half & half purified water and peroxide (to help prevent mold). Fold the paper towel closed, encasing all the rose seeds in the moistened paper towel. Then place the towel full of seeds into a plastic zippered bag. Mark the seed variety and date on the outside of the plastic bag with a permanent marker, and then place the bag into the refrigerator set at about 34-38 degrees. Never freeze the seeds, and do not let them dry out. The moistened paper towel should remain moist in the closed plastic bag for many weeks.
So grandma had the right idea in the first place, and she really did know what she was doing. It has always been fun to start roses from cuttings. Some people get their kicks by going "rose rustling" in the deserted cemeteries of old and forgotten mining towns. Others just take a twig from their favorite rose and stick it into the ground in their backyard. There is nothing complicated nor scientific about taking cuttings of roses and rooting them to "start" a new plant. There are various ways of taking rose cuttings, so let's tell you how.
Soaking the seeds is a crucial step if your seeds will germinate properly and stay clear of any diseases. You MUST not mix the bleach with the hydrogen peroxide as this results in a chemical reaction. 3% peroxide for 24 hours is just fine. This is also a good time to perform the water float test. Remove all seeds that float as they might not be viable.
Select the pollen parent flower. Remove the petals and harvest the stamens -- the male flower part that has the pollen -- as in the previous two steps. Check the stamens immediately to see if they are producing fluffy, mature, yellow pollen. If so, proceed to pollination. If not, look at stamens in the vials daily. Use them for pollination when mature pollen is coming loose from the stamens.