Driving is only 7 minutes between the zoo and the hotel. If you don't have a car, you can easily get an Uber or Lyft to take you for cheap. Easy peasie!
I concur with Jeremiah above. Uber/cabs/rentals and I bet they have a shuttle.
Taxis, Uber/Lyft, public transport, but I am not sure if there is a shuttle from the hotel to the zoo. There is an indoor parking garage if you want to rent a car though.
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