Elisa,
Thanks for writing me back!
So that is a tough one. You are right in guessing that even if a bus picked you up right at 9, it
might get you to
Disney Springs on time, but there is a fair chance it would not. Even though I typically find the ride is less than 46 minutes, it is not that much shorter that you could rely on getting there on time. Technically your solution is to do what you said in your first question you had hoped to avoid, using a taxi or ride share. Unfortunately, that may be your only reliable recourse.
I do have one other suggestion, but it is not a guarantee. While I have not stayed in the
Walt Disney World Swan Reserve yet (I am jealous, by the way!), I have stayed numerous times in both the Walt Disney World Swan and the Walt Disney World Dolphin. I have found their bell services teams on all visits to be extremely helpful. They might be able to help you out, even though your route falls outside of the normal Disney transportation routes.
I am sorry I cannot give you better advice than that, but I think it is the right information, and better to know and plan ahead than be late for your fun Disney Springs activity.
BONUS TIP If you are going to use Uber or Lyft, I find that Lyft has more cars available on property throughout the day. You are more likely to score a timely ride share with them, in my experience.
Good Luck, and I hope the Bell Services team can help you out.
Doug