There are a number of reasons your African violet could end up without roots. It may have developed a long neck or multiple crowns and needed to be broken down. I have always had good luck with planting the AV in a small pot and covering it with an inside-out zip-lock baggie. This forms a mini-greenhouse. After a couple of months check to confirm the plant is solidly rooted and remove the baggie. I will also do this if the root system seems to be a bit weak and want to be sure that the AV has sufficient moisture.
Using reservoirs is a great time saver for watering your plants. Plus, wicking can let you go for a couple weeks without worrying about them drying out. However, mineral build-ups and algae are a royal pain to clean. I line my reservoirs with white or clear plastic bags, add some water, press on the lid and then trim the excess bag. Be sure that the bags you use are completely waterproof. Many of the food bags and shopping bags are very thin and will ultimately seep. I use garbage bags and cut them to fit the reservoirs.
I usually have one or two trays of leaves at various stages of rooting or showing plantlets. However, sometimes space or time is not available to start a whole new tray. Put a couple tablespoons of whatever you use for a root starter mix in the corner of a sandwich size baggie. Prepare your leaves as usual, close the bag enough, but not necessarily air tight. I use a clothespin and clip them to my light fixtures. They can also be pinned to your curtains or any inventive way to have them near a light source. Check occasionally to be sure the medium is moist, but not too wet.Thanks to Barb Werness for both the article and the great photos!