The Approved Biographies section is the only place your bio needs to be if you want to RP. The only thing you need to do afterwards with it, is updating it when you learned a lot of new stuff and it's outdated, in which case you simply do the same thing again: post the bio, wait for approval. Your old version will be moved to the Dropped Biographies section while the new version to the Approved one.
Many RPers prefer to link their bios (and other RP threads for that matter) in their signature. The only thing you need to do is using the URL tags in your User CP > edit signature. However you are not obliged to do this. If you want to have the link appear as the name of your bio or another word, when you use the URL tags normally the link is posted twice. Just remove the 2nd link and replace it with the name/word you want to have it instead. That way it will appear like how you can see all the links in my signature.
If you click the 'How To RP' link in my signature, you can read everything about the RP if you haven't checked that thread already.