My assumption is that you -

1. Just want to fly on any private jet - doesn't matter if it is a Gulfstream or a Citation etc

2. Don't care where the plane is going - you aren't trying to get from A to B - the point is just to fly on a private jet wherever it is going
3. You want the cheapest flight you can find

if those assumptions are correct then - as noted above - you want a repositioning flight. Charter companies fly you wherever you want to go. If you want to go from A to B they have to first fly to A. If they can't find another charter to A they will sell that flight (from wherever the plane is to A) at a discount.

When they get to B they would love a charter from B to C. But if the next charter is from C to D then they will sell the leg from B to C at a discount.

Some things to think about -

You have to get to where the charter starts and get home from where the charter ends. Easier said than done in some parts of the country .

Your charter can be cancelled if the "real" charter cancels - not often a problem - but if you bought commercial tickets you could get stuck.

These flights are always last minute.