How can I make this illustration look like it's really printed on the bag?

Do you have the bag without the image overlaid?  You need that to make a good job of the displacement map.

Working with what we have got, we need to lift the image from the bag, and then paint black and white soft brush strokes that follow what shadows and highlights we can see, and continue them into the image.  This is done on a new layer.

Duplicate that layer to a new document, and blur it.  I used Gaussian blue value 20.

Save this is as your displacement map with a psd format.

Go back to your original image and select the copied image layer, and go Filter > Distort > Displace

OK the Displace panel, and it will ask you to find a file. Use the map you just saved.  This will distort the image so that it dips in shadow areas, and raises in highlight areas.

Now turn your map layer back on, and blur it some more.  I used a value of 50.

Clip it to the copied image layer, and set the blend mode to Multiply.

Reduce the opacity to give a nice shadow effect.

Copy the layer again, and set this one to Screen.  Again, set the opacity to best effect

If I wanted to take this a stage further, I would give the image layer a texture to match the bag, but do this before displacing, and merge the texture and image layers, and displace the merged layer so that the texture follows the reshaped image.  It will work better if you start with the overlaid image as a seperate object, or you'll see the old image peeping out from behind thge displaced layer

Using a displacement map will work.

You might want to play with layer blend modes so that some of the lines/wrinkles in the bag shows thru. Alternatively, you could use a layer on top, fill with 50% gray, set the layer to a blend mode of overlay - clip it to the layer with either the text or image (or group them and clip to the group) and then use black/white to create shadows and highlights (remember to use a soft brush and change the opacity to build slowly). You also probably need to skew the text a little, so that it isn't straight across (under transform) as the bag isn't a rigid object. It will take some experimenting and practice, but you should get it.