Command click on the thumbnail of that layer. You should get a selection around your object/image. Now you can fill with white.
Another option is at the top of the layers panel are some icons. One of them is to lock the transparency. Click that icon then you can fill with white and it will not affect the transparent portion of the image.
If command does not work try option. I am on a windows system, so I could easily get the modifier keys mixed up.
Ahh, OK. A background layer does not support transparency. So drag that padlock to the trashcan. (If this is CC you can just click the padlock)
That will convert the background layer to a normal layer.
Now you can use the quick select tool or the magic wand tool and select the black portion. (if you find it easier to select the white go ahead) Just as long as one or the other is selected.
Now you can invert the selection if necessary so the white is selected. Select>Invert
press the delete or backspace key to remove the white, that will leave a transparent background (looks like a white and gray checkboard)
If your selection is now gone, you can now option-click the thumbnail in the layer, to select just the black or use the transparency lock at the top of the layers panel.
Now fill with white.
Just a reminder that white will only work for screens and normally can not be printed unless you use a special printer that supports white.
Unfortunately, neither dragging the lock to the trashcan nor clicking does anything...
Just notice the top of the document window, it says bitmap. Change your mode from bitmap to rgb and then you can unlock the layer.