Just applying a blur to the selected background doesn't work too well. It'll typically halo your subject.

Here's a process that works:

First image below is the photo as shot. Assume we want a blurrier background.
Second image below is the photo with the background blurred.
Illustration that follow is a screen shot of PS (should work with most raster editors) process applied.

Here's a step by step.

Go to layers palette and duplicate the layer.
Make your selection of the subject on the top layer.
Click the layer mask icon and add a layer mask from the selection.
From the Select menu select re-select.
From the Select menu select Modify -> Expand and add 6 to 10 pixels to the selection (depends on image size).
Click on the bottom layer and from the Edit menu select Fill -> Content Aware.
Deselect the selection.
From the Filter menu select Blur -> Gaussian Blur and dial in the desired amount.
As needed refine the mask on the top layer.