I think that comments and Gonzalo's answer are correct but I want to add more informations.
First the good and natural way it's to use (node.center) if you want to draw something from the center of a node.
outer sep is used to placed the anchors (except center anchor) so it's damage to modify outer sep. Below I place a picture to explain how to use the different options.

Now in your case, there are some remarks to add. First , you use edge but if you use toand if you want to get the center of the final node, you can find another way.
The first picture shows the normal way. outer sep with line width are determined to get the start and the end of the edge near the shape of the node. The interesting case is the third one, because edge is a special operation (see the pgfmnual) and in the edge is drawn before the last node and the arrow goes to (2,-1).
\documentclass{article}
\usepackage{tikz}
\usepackage{spath}
\begin{document}
\begin{tikzpicture}
\node[circle,draw](A) {A};
\node[circle,draw](B) at (2,-1){B};
\draw[->,red,thick] (A) edge [bend left] (B);
\end{tikzpicture}
\begin{tikzpicture}
\node[circle,draw](A) {A};
\node[circle,draw](B) at (2,-1){B};
\draw[->,red,thick] (A.center) edge [bend left] (B.center);
\end{tikzpicture}
\begin{tikzpicture}
\node[circle,draw](A) {A};
\draw[->,red,thick] (A) edge [bend left] node[at end,circle,draw,black,thin]{B}(2,-1) ;
\end{tikzpicture}
\begin{tikzpicture}
\node[circle,draw](A) {A};
\node[circle,draw](B) at (2,-1){B};
\draw[->,red,thick] (A.center) to [bend left] (B);
\end{tikzpicture}
\end{document}
inner sep=0will make the border be tighter around the text. – Caramdir Apr 3 '12 at 3:33