Never tried the QV Bitmap copy approach, I use Greenshot and do screen caps for most things but just a thought from generic MS-Office issues. I find I often get better quality output from an image copy and paste if I use the Paste as Picture option, rather than the default Paste. Does this help get you better quality by any chance?
As far as printing goes not sure where you're referring to printing from, but if you mean a print to PDF from QV then try the option under the menu User Preferences - Printing - Bypass Postcript for printing (slow). Yes it is slow, but the output font quality does seem to improve with certain printers. Obviously also checking the setting in the PDF printer driver - it needs to be set to a decent dpi to get quality output - e.g. if you are using say 300 dpi try upping to 600 dpi there. You'll get a bigger file but quality should be better too.