Translation:I would like you to make your bed.
Bien acts as a "softener" when combined with the verb aimer. It makes the like/love less intense. You'd use it in everyday conversation about things that you like well enough. J'aime is stronger and just a bit more formal. With things it still means like, but when used with people, it means "love" of course.
To say that you would very much like something, use beaucoup. J'aimerais beaucoup...
Welcome to the subjunctive mood! (le subjonctif) Basically in French, when you are expressing a desire or wish on someone else, or there is an element of doubt, judgement, possibility, or necessity, you must use the subjunctive mood. Here is faire conjugated in the subjunctive:
que je fasse
que tu fasses
que nous fassions
que vous fassiez
Here are some common phrases that use the subjunctive: il faut que, il est nécessaire que, il est possible que, etc.
This is a tricky concept and there are a lot of verbs that can take on the subjunctive mood depending upon their use. Here is a site that may help explain more: https://www.lawlessfrench.com/grammar/subjunctive/