I've never tried rooting a florist rose, but I imagine it is essentially the same process as any other soft-wood cutting. If the bloom still looks nice, you can enjoy it a little longer; I'd add just a touch of plant fertilizer to the water. But eventually you'll want to cut the bloom off just a little above the top set of leaves. If the stem's leaves were all pulled off, I'd cut the stem a half inch above where the new growth is coming out. Then roughly 6 inches below that point. Be sure to use a sharp scissor or pruner (never use anvil-style pruners on roses, only by-pass or scissor style). Rooting hormone will also be very important. It comes in powder and liquid forms. Ask any local garden center. You dip the freshly cut bottom of the stem into the hormone, tap off any excess (clumps) and stick it a couple inches into fresh sterile rooting medium --some people have even used pure perlite. Don't use soil from outside or already used potting soil, as there will be more potentially harmful bacteria that can cause the stem to rot before it develops roots.
You'll need to put the stem someplace to maintain high humidity, since the stem has no roots to take up fresh water with. I use gallon-size zip-loc bags. Others use 2 liter soda bottles with the bottom cut out, placed over a little pot. The stem also will need indirect sunlight, such as in a north-facing window sill. Check on the baby frequently, every couple days or so and mist it if it appears to be drying out. Be careful not to keep it too wet, though, as that invites mildew. Rooting often takes 4 to 6 weeks, but it can be a little quicker or take much longer.
Do a search on this forum for rooting cuttings. There are a few different methods people use, and different folks swear by different methods. It's partly trial and error. Good luck!