"I would like you to make your bed."
Translation:J'aimerais bien que tu fasses ton lit.
Je voudrais sounds like a wish. If my mom told me this, I would answer Et je voudrais un million de dollars. You can use it for orders, but it sounds really formal. It's the expression traditional teachers use, or people in a fancy restaurant/hotel...
J'aimerais bien is more casual. You shouldn't use it in formal situation, but you use it with your family/friends. You can also use it for wishes, but achievable ones J'aimerais bien aller à la plage for instance.
Actually I'm thinking of some situations where it makes a difference. If you ask a waiter "Je voudrais du pain" as he forgot to bring some, it will sound nicer than "j'aimerais bien du pain" which will sound more ironic and a bit mean. I think "j'aimerais bien" is a way to avoid saying directly to someone you're giving an order, so sometimes it can make you sound like someone who isn't really sincere.