Hi Evvie,
I'm happy to help you navigate from Magic Kingdom to the
Bibbidi Bobbidi Boutique and back during your Walt Disney World visit. I wouldn't bother returning to Pop Century to make the transfer to a bus to Disney Springs. I think that would extend your journey.
If your appointment is before 4 p.m., as I assume, I would simply walk from Magic Kingdom to the
Contemporary for a direct bus to
Disney Springs. (Direct service from the Magic Kingdom to Disney Springs begins at 4 p.m.) The walk will take you just about 10 minutes and you will reach the bus stop right before the doorway for the resort.
When you are finished with your appointment, you can easily hop back on a bus to the Contemporary and reverse your path to
Magic Kingdom. I've found it's easier and often faster to walk between the Contemporary and Magic Kingdom than to use the monorail or a boat.
I would allow at least an hour to get from inside Magic Kingdom to Disney Springs. You certainly don't want to be late for your appointment.
Thanks for visiting the Disney Parks Moms Panel, Evvie. Please let us know if we can answer any other questions for you as you finalize your plans.
Enjoy,
Wilma