Easiest way to go to Wild Wadi is to use a taxi/cab.
Prices are different from each side of Dubai for going to WildWadi WaterPark. From Deira it costs about 70-100 AED using a free cab/taxi and it costs about 50-80 AED if you use Careem or Uber there same price from Bur Dubai to the park.
Hotels in Sheikh Zayed might costs about 40-80 AED if you use Careem or Uber. Also it take 15-20 minutes to arrive at the park.