Echoing a lot of what was said already. Don't go back for another undergrad degree if business is your next focus. An MBA would be the way to go to do the career switch into business.
My advice as a previous MBA grad is to figure out WHY you want a MBA (other than just a career switch) and WHICH area of business you would want to focus on. I can tell you from the get go (as an alumni interviewer), that without a clear focus as to WHY you are looking to get an MBA, top-tier business schools won't consider you as a candidate. This is because, like undergrad, there's more to a good MBA program than just your course material, you'll be meeting peers that will provide you with a network of opportunities and support during and after you graduate. An MBA program is typically a substantial financial and time investment, so it's not a decision to take lightly.
Most people approach the application process with a goal in mind along with a business focus, e.g. "I want to become a marketing manager", "I want to become an investment banker", "I want to become a consultant", etc. A good program will help you focus and achieve those goals. You're certainly not locked into your decision once you get in, as many people shift gears once they get their hands dirty, but without a goal and vision, it's difficult to get in the door.
As for having a psychology degree, providing you have some achievements to speak for during your post-undergrad years, the degree can be an asset to your application process. Just today, I had a meeting with a consultant who was a professor of psychology at various top universities before jumping into the private sector as a consultant. He doesn't have a business background at all, but is well respected for being able to bring a different perspective to the table and to apply his psychology background to move his clients' businesses forward.
There are other ways into the business world WITHOUT having to get an MBA. If you're interested in going into organizational development, organizational behavior, or HR, pickup the phone and call some people in the field to do some "informational interviews". They can help point the way to how you can enter those fields at the entry level and learn as you go. Consider it "paid tuition". Also, marcom/PR (marketing communications and public relations) people I've met have mostly come from a variety of backgrounds that you wouldn't have thought "business" when you find out what they are.
There's lots of opportunities out there. Since this is a major shift for you, take your time to figure it out before you jump.
EDIT:
How many years of professional experience do you have currently? Top programs expect at least 3-5 years depending on your level of achievements during your professional life. If you're qualified there, don't worry about not having the academic background, as long as you're a motivated achiever. We had a pianist in my class who is a high achiever and ALWAYS was able to pull her weight in team projects.