Hi Brandi,
I love
Sanaa! This restaurant features delicious Indian-inspired cuisine. You can indeed take
Disney bus transportation between resorts; however, you will need to change buses to do so. For the trip that you are considering, you could take a bus from Disney's Saratoga Springs Resort & Spa to Disney's Animal Kingdom Park, and then change buses there to catch a bus to Disney's Animal Kingdom Villas - Kidani Village. This is easy, but could take some time as you might have to wait for each bus. I would leave at least 90 minutes for this journey.
There is one way to do this trip without taking two modes of transportation, and that is to use Disney Springs as your transfer point. You can
walk to Disney Springs from Disney's Saratoga Springs Resort & Spa. This can be a healthy distance from some points in Disney's Saratoga Springs Resort & Spa, so do check where you are within the resort. The walk to Disney Springs is the shortest from the Congress Park area. If you are further away or do not want to walk, you can also take a boat for this leg of the trip. From Disney Springs, you can take a bus to Disney's Animal Kingdom Villas - Kidani Village.
Check out the bus transportation link I provided above for information on how late buses run. If your reservation is late, you might need to use Disney Springs as your transfer point as it is often open the latest. Also, you can always ask a cast member in the lobby to call a taxi for you. This will come with a cost; however, I have found taxi rides around Walt Disney World to be reasonable. This will take you door-to-door.
Please do let us know if you have any further questions, Brandi!