To say that Business is helpful in Art and Design specifically wouldn't be entirely accurate, because there is so little overlap between the two.
Business Management will certainly provide you with useful skills for starting any kind of entrepreneurial affairs (not just Arts and design). If you want to get a head start and get a taste of how running a business is, then sure, by all means, take it. But do be aware that the information you learn at this level is still quite introductory and that you will, if you choose to pursue if further, have to study much more advanced materials later on. Even if you don't take Business now, there'd still be plenty of time in the future to take on the subject. Most unis that offer Business courses don't usually stipulate Business Management as a requisite.
I'm not exactly sure how Psychology would come in play here. I mean sure, it may provide some insight into human motivation but it would be a very small part of Human Resources, if anything. The focus of Psychology as a subject is not to make money or help run a business if that's what you're after.