Police only "bully" citizens because of drug prohibition. Before that police was seen similarly to firemen...helpful folks that are keeping a place safe. Once drug prohibition started, the monetary reward for corruption and opportunity to profile people came about. Around that same time, people started feeling less safe in the presence of the police. Look at the police in Portugal, where are drugs are criminalized. They're cool.
Cops are cool everywhere in the European Union, and not just in Portugal (perhaps with the exception of certain eastern European nations such as Poland and Lithuania). The difference in the United States is due to the cultural variations.