1) Create a background rectangle on a new layer (at the bottom). Using the bucket tool and fill with any color. Then remove the borders.
2) Scale the background to fit the work area (canvas).
3) Import the bitmap and place on the work area.
4) Use Modify > Break Apart to create a Bitmap Fill.
5) Use eye-dropper on the Bitmap Fill. Note it picks up the texture.
6) Use the bucket tool to fill the background rectangle.

Note the target shape doesn't have to be a background, rectangular or cover the whole work area. However the fill will be repeated as if it were.