Why refrigerate bagels after shaping dough?
It doesn't matter as far as rise or flavor is concerned.  You can cold rise the dough, or the shaped bagels, or both.

However, the advantage of cold-rising the shaped bagels is that the cold dough is easier to peel off and dunk in the boiling water than room-temp dough is.  Bagel dough tends to be sticky and soft, and it's challenging to avoid stretching the bagels while dunking.