Hello, Alice!
This looks as if you've found a perfect Plan B!
As soon as the Fairy Godmothers-in-training are finished with your little princess at Bibbidi Bobbidi Boutique (which is tucked inside the World of Disney Store at Downtown Disney), I suggest that you head to the bus stop and take a bus to one of the resorts that are on the monorail. If you choose Disney's Contemporary Resort, you will also have the option to take an easy walk to Magic Kingdom Park. (My family of four usually takes under ten minutes, from resort to bag check, walking at a leisurely pace.) However, Disney's Grand Floridian Resort & Spa is the last stop on the monorail before it heads to Magic Kingdom. Heading there will ensure that your monorail will take you directly to Magic Kingdom Park, saving you the time it takes to stop at the other monorail resorts.
Take a look at this Walt Disney World transportation map, if you'd like a visual aide. In the top, left side, you'll see the monorail line (a blue and yellow dashed line) which loops from Magic Kingdom Park to each of the three monorail-accessible resorts. On this map, the monorail runs clockwise.
Again, I'd leave Downtown Disney as soon as your princess is finished with her transformation. Although most resort buses run every twenty minutes, there are always occasions when something comes up, and your perfectly-timed adventure takes a little longer than you had planned.
I'm sure that you will have a fabulous day, and the Princesses are sure to make a big fuss when they see a visiting princess in their midst!