For future reference, these types of questions arise all the time here. No one person here is an expert on all the transportation options in Orange and Los Angeles Counties. The fastest way to get accurate information is to do what I did - go to
metro.net and use the trip planner.
There are three possible combinations of buses listed for the trip from DLR to AotP. You should use enter the time and day you want to arrive at the aquarium to find out your options. Unfortunately, the journey will take a long time - the shortest itinerary I found for a particular Saturday morning trip is listed as taking 2 hours and 19 minutes.