Fill a 6-inch diameter pot with a sterile, soilless potting media. A potting media that contains peat and vermiculite works well for propagation. Water the media until it's evenly moistened and the excess water drains from the bottom of the pot.
Cut a stem from the China rose that has just completed blooming, using bypass shears. Dip the bypass shears into a solution of 1 part bleach and 3 parts water to disinfect them between cuts. Cut the old flower head off the selected stem with a straight cut just above the topmost set of leaves. Make the second cut 6 to 8 inches down from the tip at a 45-degree angle, making the cut above a leaf set.
Pull off the leaves on the stem, leaving only the topmost leaves in place to fuel the cutting. Place a small amount of a liquid or powder rooting hormone in a bowl, and dip the bottom of the stem, with the angled cut, into the hormone so it's completely coated.
Insert the bottom of the cutting into the potting media. Bury the bottom half of the cutting so the stem remains upright.
Insert a stick into the media on either side of the cutting, using sticks taller than the rose stem. Set the pot in a clear plastic bag and gather it closed at the top, securing it with a clothespin. The sticks prevent the plastic from touching the cutting.
Set the pot in an area that receives bright but indirect sunlight. The bag retains moisture so the cutting rarely requires watering, although you may need to irrigate lightly if the soil surface begins to dry.
Remove the bag once the cutting roots and new leaves begin to grow. The original leaves may wither and die just before new growth appears. Continue to provide the new China rose plant with bright sunlight and water it when the soil surface feels dry. Water at the base of the plant until the excess drips from the bottom of the pot, indicating the soil is moistened throughout its depth. Empty the drained water from the drip tray beneath the pot after watering.