Yes, it is doable. We have many members here who have done just that in order to get some of the florist roses that aren't available for sale as bushes. There are many ways of doing it and if you do a search on here for rooting roses I'm sure you'll find many threads with detailed instructions. Here's what I do. It doesn't always work but it might be worth a try.

You will need some clear plastic 16 oz. drinking cups with a good hole punched in the bottom, some type of rooting hormone, some seed starting soil, a pair of sharp scissors or a knife and a pencil. Prepare the cup first. Make sure the hole is poked and open so water will drain out of the cup easily. Fill the cup with the seed starter soil and make sure it is very damp but not soggy wet. Once you have that take the pencil and poke a hole into the soil for the stem to go into. Put it in deep but it does not have to go all the way to the bottom.

Once the bloom has faded remove just the top spent bloom from the stem. Remove any leaves from the portion of the stem that will be in the soil. You can leave or remove the leaves above the soil, it doesn't matter. At the bottom of the stem take a sharp knife or scissors and carefully cut the stem at a very steep angle then scrape off the green outer layer of skin around the stem to expose the white inner layer up maybe an inch or so. Dip this end into the rooting hormone and shake off any excess. Place the dipped end into the hole you made with the pencil. Making the hole ahead is to prevent the hormone from being removed when you stick it in the soil. Then pat the soil back down around the stem firmly. I usually tap the bottom of the cup on the table a couple of times to make sure the stem is firmly settled and has full soil contact. Put the cup in a sunny place and keep it evenly watered. You want it continuously damp but not soggy wet or it will rot. Do not keep a tray or saucer under it because that will hold water up in the cup and the stem will rot.

Now all you have to do is wait PATIENTLY. It can take several weeks for it to root. As long as the stem does not dry out or turn black it's fine. You may see some leaves start to sprout early on. That does not mean the rose has rooted. Roses store energy in their stems and can produce leaves from that energy. RESIST the urge to tug on the stem to see if it is rooted. The reason for the clear plastic cup is so that when the rose has rooted well you will be able to see the roots through the sides and bottom of the cup. Once you can see a good amount of roots around the cup you can go ahead and pot it up into a larger pot.

I would keep it potted for maybe the first year depending on how fast it grows. KEEP IT OUTSIDE!! Roses are not house plants and hate the conditions indoors. If you live in a cold zone either sink the pot in the ground in a very well protected place and cover it with mulch or put it inside an insulated but unheated garage for the winter. If you garage it for the winter you must remember to water it every month through the whole winter until you can get it back outside in the spring. Once you think it's large enough you can plant it in the ground. Roses love full sun and about an inch of water per week. Fertilize about once a month.

I wish you great success and lots of roses!