I tested your code from www.gulin.sg/tests/mouse12.php and it would not do it on same line for me either. Then I added a DTD (Document Type Declaration) to the top and it worked then. Having a proper DOCTYPE is important in many many cases!
Even though your code worked (with a proper DTD) I made a few changes to it to offer you a bit more modern and simpler code:
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<meta content="text/html; charset=ISO-8859-1" http-equiv="content-type">
document.body.background = aa;
document.getElementById ("hid").style.display = bb;
<a href="#" onmouseover ="showtext('images/image.jpg','inline')" onmouseout ="showtext('','none');">Beginning of Sentence -
<span id="hid" style="display: none; width: 100%;">
hidden and shown on mouseover on same line as beginning
Note I changed the span's id shorter to "hid", and in this case using the span is correct.
Note that I moved the image and it's path out of the script and in to the onmouseover function call, this way you will be able to easily change that in different mouseovers in your page if you want. And 'inline' is the display property being passed in the mouseover, could use 'block' instead in different applications to show a hidden element, but if used here it would start a new line.