Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.
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.
After the rose seeds have soaked overnight, rinse them in a strainer and place them into the blender with at least a cup of plain purified water (making sure all seeds are covered), and turn it on for a few minutes. It usually doesn't chop up the seeds, but rather, it will clean off the pulp remaining from the rose hip, which would otherwise mold if left on the rose seed. You may see a few seeds chopped up, but those usually aren't viable anyway. Flush the rose seeds again through a strainer using fresh purified water.   
The Misting Method: As you get more sophisticated in your rose propagating methods you may eventually want to set up a misting bench. It can be an open-air bench or one enclosed in a greenhouse, or even a small misting box, similar to the one my husband Bob built for me. (Refer to "How We Made Our Misting Box," from Rose Ecstasy. You could choose to rig it up with a manual or an automatically-timed mister, whatever your time, money, or expertise will allow. I am fortunate to have a very handy guy for a husband, who is a good sport whenever I come up with these crazy project ideas.

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.   
While your cuttings take root, keep them covered and moist. In a garden bed, a simple DIY mini greenhouse does the trick. Just place a bell jar, a garden cloche or an overturned mason jar over the cutting. A clear plastic bottle with the bottom cut out and the cap removed works, too. Water the soil regularly to keep it moist, but not soggy. Your mini hothouse will keep the humidity high inside.
Español: cultivar rosas usando semillas, Italiano: Coltivare le Rose Usando i Semi, Português: Cultivar Rosas a Partir da Semente, Русский: вырастить розы из семян, 中文: 用种子种玫瑰, Deutsch: Aus Samenkörnern Rosen ziehen, Français: faire pousser des roses à partir de graines, Nederlands: Rozen kweken uit zaad, Bahasa Indonesia: Menanam Bunga Mawar dari Biji, العربية: زراعة الورود من البذرة, Tiếng Việt: Trồng hoa hồng từ hạt, 日本語: バラを種から育てる, 한국어: 씨앗으로 장미 기르는 방법
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