A few, they can be found in the Warm Springs HMA, south of Burns, along with an occasional mule. State route 205 marks the eastern boundary of the HMA, second largest in the state.
The target population density of the HMA is 0.42 animals per thousand acres (based on upper range of AML), compared to a state average of 0.97. The likelihood of actually seeing a burro or mule in the area is small, unless they tend to hang out in one place and you know where it is.
A WHB specialist based in Burns or Hines may be able to help you find them.