I would like to use the bevel tool on just one edge of an object rather than having it effect every face. Can I do that?
I’ve tried edge and face modes and I get the same results.
Nah, you can’t, sorry.
Now I’m sad. 
yes you can.
in edit mode, select your edge, then in the scripts window (split your screen if necessary), click scripts>mesh>bevel center.
I’m trying that but it’s giving me a bunch of errors.
Look in the python forum for my topic on bevel center, it has the link and code of the corrected version but I never got it to work.
If you just extrude a Face and then smoth it a couple of times, you got the same effect without a script…