Qualifications
The incredible variety of jobs available for professional bureaucrats also means there are a wide range of qualifications and kinds of training expected of you. Some positions require little more than an associate's degree, while the senior-er positions will need at least a master's degree for you to even be considered.
Public administration is one important field of study (obviously), but so are finance, political science, and management. You might need decades of experience in public service to get some positions, while others like market research can be done right out of college.
Besides what's in your head, what makes a good public administrator is also what's in your heart (aww). You've really got to care about people in society in general, because people in society are what you'll be dealing with on a daily basis. Communication is key.
Much like an awesome giant robot, bureaucracy only works when all of its parts are working together, otherwise everything could fall apart―and then you've got falling robot pieces to deal with.