Unfortunately, I cannot reproduce the problem, so I can't suggest a fix. Is the header there if you try to print it? It might be a 'ghost' you are seeing as you say you can't select it or delete it.
The styles use HTML and CSS to create the output which is then converted to WordProcessingML by Word. The layout you want can only be achieved in two ways when using HTML: either by using a table with 2 columns or by using divs which are positioned next
to each other. Of those two solutions, only a table is feasible as it can adjust the width of an entire column as needed. If you would use divs, you would have to hardcode widths depending on the size of the font you are using and the number of sources you
have in your bibliography ( requires less space than  so the entire alignment would have to shift).
With divs, your layout for 1 entry would be something like:
<div class='source' style='position:relative; clear:both;'>
<div class='column1' style='position: relative; float: left; width: 10%;'><p></p></div>
<div class='column2' style='position: relative; float: right; width: 89%;'><p>Lastname, Firstname, ...</p></div>
The classnames source, column1, and column2 are only for illustration purposes here.
I currently have no intention of implementing the above scheme myself, but if you want to give it a try, the easiest is probably to overwrite the following template functions in the xslt:
- format-bibliography-as-table: you could get rid of the table element. The tr elements should be replaced by the div of class source in the above example;
- format-bibliography-table-column: here the td elements should be replaced by the inner divs from the above example. Their style attribute would need adjustment based on the column you are displaying.