A private jet flight from San Francisco to San Jose (35 miles) produces more carbon per passenger than a commercial flight covering ten times the distance. Short private jet hops exist primarily because the people who can afford them find them convenient. That's fine. Convenience can be taxed.
The formula: set a minimum threshold distance (100 miles)and then for any flight logged below that threshold, charge a carbon tax of $100 per mile to bridge the gap. So for a 35-mile flight: 100-35=65, multiply that by $100 and you get a $6,500 carbon tax. The flight remains legal, if not perhaps 2x as expensive to avoid sitting in traffic. It just costs more, and that money funds something useful for the government. This literally only impacts impatient (or self-important) people who take short, bad for the environment, flights. The vast majority benefit and the folks who can afford to pay, do.
If the flight is worth the tax, take the flight. If it isn't, take the highway. The market can sort this out.