One way is to think of the background as a 'grid' of
connecting tiles. So, if for example your stage was 800px wide and
400 pixels high, you could treat it as a grid composed of 40px x
40px tiles (20 tiles wide, 10 tiles high). Each game cycle you draw
the tiles, but offset them to simulate the movement. When the tile
has slid all the way off-screen, you forget about it and randomly
select a new tile to show.
For a really simple example, create 3 bitmaps that are 40 x
40px and call these tile1, tile2 and tile3. Set the movie size to
800px x 400px and put the following behaviour into a frame script
and hit play.