In recent years Disney has eliminated most of the direct buses from Disney Springs to the various Parks. This happened about the time that they changed from Downtown Disney to Disney Springs. However, the bus is do run to all of the Resort's so worst case scenario you can take a bus to one of the Resort's then transfer to a bus going to the parks. I've used this method with great success over many years. I typically stay at Bonnet Creek about a mile or so away from Disney Springs so park for free and use the complimentary Disney transportation system.
As far as I can remember there is a bus you typhoon lagoon from Disney Springs!
If I remember correctly, you can get on a bus that goes to Typhoon Lagoon from Disney Springs. You may be able to head that way from Animal Kingdom as well.
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