Asari biotics are not developed independent of exposure to element zero. That's impossible in the Mass Effect setting. It's more likely that Thessia, the asari homeworld, has element zero in its planetary makeup (in addition to the standard stuff like iron, nickel, etc.), exposing all life on Thessia--including the asari--to element zero and thus giving them biotic abilities. That means asari probably even have a little element zero in their own bodies, similar to how humans have iron in theirs.