I've always heard of people using Lyft and Uber, which is a safe bet. I personally wouldn't use public transportation in Orlando, as I personally never used it before and Orlando is shady.
Also, I do not believe there is public transportation from Disney Springs (but someone can correct me if I'm wrong), but read there is a Lynx bus for MK. Even then there would be transfers.
I would post one of the articles I read on here, but I do not know how accurate / how up to date it is. Either way, if you want a quicker, safer, more efficient route, I would just pay the few extra dollars for a Lyft, or Uber.