Are you sure you are looking for info on resolution 1280x768 and not 1365x768 (16:9 aspect ratio) or 1024x768 (4:3 aspect ratio)? Below are the resolutions and related aspect ratios that I know of:
List of 4:3 Monitor Resolutions
Resolution - Aspect ratio
640x480-----4:3
800x600-----4:3
1024x768-----4:3
1152x864-----4:3
1280x960-----4:3
1400x1050-----4:3
1600x1200-----4:3
2048x1536-----4:3
3200x2400-----4:3
4000x3000-----4:3
6400x4800-----4:3
List of 16:9 Widescreen Resolutions
Resolution - Aspect ratio
852x480-----16:9
1280x720-----16:9
1365x768-----16:9
1600x900-----16:9
1920x1080-----16:9
List of 16:10 Widescreen Resolutions
Resolution - Aspect ratio
1440x900-----16:10
1680x1050-----16:10
1920x1200-----16:10
2560x1600-----16:10
3840x2400-----16:10
7680x4800-----16:10
We can't really check for you if there are black bars or not since it really depends on your display, and we may have different displays.
Check your display's aspect ratio (4:3, 16:9, 16:10) and max resolution settings, then cross-check the appropriate resolution settings for it. If you use a resolution setting that does not match your aspect ratio, then you will definitely get black bars on your display's borders.
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