That's what happens when you resize an image. Unless your original image has the same aspect ratio, when you resize it, one of the measurments will be a little off. Here's an example:
If you have an image that's 100 pixels wide by 100 pixels high, the aspect ratio is 1:1 (or 1 as expressed in PSP). Your original image is 105x104 which is an aspect ratio of 1.0096 and your new size of 80x79 is actually an aspect ratio of 1.01265. This creates the distortion, not to mention the fact that your original file is only ~72dpi.
Personally, I work with master files that are HUGE, at least 1500 pixels wide. When I resize those down to what I need for web publishing (which is usually ~200-500 wide) I get little if any distortion with my resultant file.
While your bitmap trick does create less distortion, there is still pixelation of your resultant file, especially around the text parts.
Good luck,