Hi & welcome! Does your cutting have roots already? If not, I would wait until you see them to move it to a pot of soil. The roots of this plant can be very substantial, so don't choose a tiny pot.
Over time, plants in bottles/jars of water tend to get chlorotic and weak, so it doesn't work as a permanent setup for most plants. I've kept cuttings of this one in bottles of water for up to 6 months. Like any member of Commelinaceae family that I've experimented with, cut stems make roots easily in water. If you notice any discoloration, cloudiness, or odor, change the water.
Tap water can have different substances in it, depending on the local facilities and practices. Many plants can be sensitive to fluoride in particular, or the high PH that tap water tends to have. These issues can come into play whether a plant is in just water, or in a pot and being given tap water. I haven't encountered any info about Tradescantia plants being especially sensitive to fluoride, and haven't noticed any sensitivities among my own plants.
