Thanks for the correction, Zocus! The truth is, I know that от requires the genitive, not the accusative! But I first wrote собака избегает ванну, but I wasn't sure if that was correct to use the accusative with избегать, so I changed the verb to убегает and added the от, but forgot to change the case of the object noun.
But anyway, when speaking about washing a dog, is there a better noun to use than ванна? I don't mean that the dog is afraid of the bathtub or the bathroom; I mean that the dog does not like to be washed with soap and water!