Can there ever be real political change without bloodshed?

Yes. Though the speed of change happens on very different scales. It's important to note that neither way is a reliable method to get the results you may want though. We can look at FDR's new program and how it saved and rebuilt a middle class in the US, but was then gradually reformed away by the wealthy to once again favor the rich. Most revolutions have ended up fairly unsuccessful. Trading one set of problems for another, and often times one set of rich people for another.