There are a lot of different areas of robotics (controls, mechanical design, dynamics, stability, motion planning, etc.). Find what you're interested in and take courses in it is the best place to start. There are several paths in robotics: mechanical design where lots hands-on projects and a portfolio helps; theory/algorithms where getting a masters/phd is helpful, also human-robot interaction where running user studies and statistics play a huge part. My advice is to do project-based work like a senior capstone and take as many robotics courses as you can. Also building robots with motors, sensors, and actuators for fun will also give you hands on design experience. Stop by a machine shop and get certified to use the equipment. That being said, I've known people who go to work after their bachelors (generally had an internship at the company or had done research as undergrads).
I personally worked in underwater robots as an undergrad and had broad exposure to going on dives, data collection, and small projects. Then I did a senior design project building a teleoperated robotic arm with force feedback. I'd taken mechatronics and loved building things. A bachelor's would have been enough to get a job at a robotics company, however, I wanted to get into design and gain a more solid foundation.
Robotics is a specialized field with a lot of math and theory behind it. I would strongly advocate a masters. It gives you more exposure, more training and projects, and will enable you to ask for a higher salary. If you're interested in working in a research lab or becoming faculty, go for the PhD. Most companies who specialize in robotics are heavily focused on design and product development and have more of a mechanical engineering background.
This response was contributed by Dr. Fitzgerald's friend Ms. Carol E. Reiley, PhD Candidate, Computer Science, Johns Hopkins University.