I did not go into the game development/design field, however some of my best friends from college did go into these fields and I can say that from what I've heard, a bachelors degree and passion for the art goes a long way. Try determining what aspect of game design you like the best, is it game project management, writing, art & animation, programming, etc? Once you figure out what you think you would enjoy the most, try looking at schools or online courses/classes that focus in your desired area.
Additionally, being passionate about what you do is definitely very important. If you're excited about what you're working on every day, others will pick up on it and will want you to be a part of their team.
Hope this helps!