When I was in junior high school, my biology lab partner was a girl named Wendy. She was really cute, but I was too shy to every let on that I noticed. I hardly ever saw Wendy after junior high, but I heard about her just after New Year's Eve a couple of years ago. She had been leaving a party and walking to her car when a bullet fell out of the sky, killing her instantly. Someone had fired that bullet into the air to celebrate the new year, never meaning to hurt anyone. But Wendy's life was ended, and her family had to deal with this unimaginable challenge. This included the financial burden of medical bills and funeral expenses.
Wherever you stand on the right to bear arms, chances are you would agree that people also have a right not to be injured or killed by a randomly flying bullet. Having to bear the financial costs is literally adding insult to injury.
It would be a simple matter of statistics to determine what kinds of injury and damage are caused by each type of ammunition, and add a per unit fee to go into a fund to pay property damage, medical and funeral expenses to those who (or whose survivors) can demonstrate "innocent bystander" status. Ammunition dispensed and used in a closed shooting range would be exempt. And gun owners would only bear additional expense based on the amount of ammunition purchased. For true personal safety usage, this amount is likely to be low.
There are risks associated with living in a society with gun rights, but the fairest approach is to require those who choose to own guns to bear greater responsibilities.