The fuel rates are currently about $0.22/gallon, and are going up to $1.06/gallon over 5 years, but even that wouldn't put them on par with commercial flights (they pay 0.6% of the fees, but use 7% of resources, $1.06 divided by $0.22 gets you 4.81x the current 0.6%, which is still 2.9% of the fees, while using 7% of FAA resources.)

So even with the current fuel rate increases, private jets would still be paying less than half of what they end up using.