The best option I can think of is to save the current view/map extent to a raster file and check the option to also save a georegistered tab file with the image.
In this way, you can open the image into your map window again afterwards and use it as a background map.
Also consider changing the resolution of the image, you are creating to get a bit more details. But you must still be aware that it will only hold the details for the current zoom and zooming into the saved image will not give you more details.
Also take note of the Bing Term of Use that can be found on the Bagstage (the PRO tab) under About.