The div #bunting includes all the login links etc, and has the background image. Try making the css:
Code:
#bunting {
background: url("/image/bunting.png") no-repeat scroll 0 0 transparent;
/*height: 61px;*/
margin: 0 auto;
position: relative;
width: 880px;
/*z-index: 9999;*/
padding-top:61px
}
z-index isn't going to make any difference because #bunting contains all the elements you're trying to rearrange. Giving the element padding-top pushes the content down without changing the position of the background, and setting no-repeat means the image will only show once.
EDIT: Reading your post again I'm not quite certain that's the effect you want...if you just want the bunting to be on top of #container then you need to rearrange your html so #bunting doesn't include #container. Then you can use z-index to position it on top of #container.