From CSR to AKL you are looking at a very reasonable cab rate. I would put it around $10 plus tip, they are very close to each other.
What I do when I don't want to pay for a cab, regardless of which resort I stay in, is get on the first bus I see. If its at night, DTD busses come regularly but you will see several park busses most likely before a DTD one. During the day or early evening, any park bus will be just fine. I just grab the first one, no need to wait for a different one, even if its a park that is closer to the resort you are going to.
For the record, last June, my family and I went to WDW his family. His aunt hurt her knee and getting on the busses was tough. One night we needed to get from ASMU to AKL. Because we needed a van to seat all six of us (which didnt' work for her knee problem) and because because I didn't want to pay for two cabs, I just took my kids by bus, to MK, then hopped off and easily got over to AKL stop and in no time a bus came. Dh went from our room, to the front of the resort, they called a cab, the driver took them over and we actually had beat them. Even with going all the way over to MK and switching busses, the kids and I beat them there.
Cabs can be very nice, but they aren't always a sure way to get there faster.