How to blur edges outwards of an image in Photoshop?

I'll add my two cents worth...

The lady's right hand is very close to frame edge, and I wouldn't want to mess that up, so I would start by filling the border with Content Aware Fill.  Rather like we do when faking some extra content when preparing a canvas print we will need to fit round the stretcher.  Then use a feathered layer mask as per suggestions above.

I'll add that the lens blur options are different from things like Gaussian Blur, because they don't cause selected content to bleed outside the selection.

Hello everyone!

Just want to say thank you for the help! All of your tips really clarified the problem.

Thanks again!

I assume you have the image on a layer above a black background layer as shown here.

Click on Layer 0, which contains your image. Then select the Elliptical Marquee tool, and in the Options bar, set Feather to 0.  Select part of the image. To reposition the selection, click in its center and drag it. Note: If, after creating the selection, you want to alter its dimensions, choose Select > Transform Selection, and make the adjustment. Then either click on the Commit checkmark in the upper right of the Options bar, or use the Return key to complete the change.)

Still in Layer 0, click on the Add Layer Mask symbol at the bottom of the Layers panel. It is the second symbol from the left. This will produce a hard-edged oval containing the selected portion of the image. Choose the Properties panel, move the Feather slider to produce the degree of vignette you prefer and click OK. If the Properties panel does not currently appear, choose Window from the Menu bar and click on Properties from the drop-down menu.

If you have PS CC, you can use Iris Blur.

I would recommend using a Layer Mask and Feathering that.