All this boils down to how much money you have to spend.

Everyone here focused on Lear, and keeps telling you they are flown by
two pilots. True enough, but the fact is that Cessna makes a single
pilot Citation jet, and quite a few people own those as personal
self-flown airplanes. So assuming that's what you're going for (a
6-person 450-mph jet) here's what you need to do:

Get your private, instrument, multi-instrument, and Citation type
rating in that order. You will probably need to rack up some multi
time before anyone will try to teach you in a Citation. All of this,
including the practice time required, can probably be made to happen
for less than $120K in under 500 hours. If you push it, you can
probably make it all happen in a year or so. If the price tag is out
of reach for you, you can't afford the private jet anyway.

If in the process you buy a transition airplane (most likely a twin -
something like a Cessna 310 that is reasonable for training but has
adequate performance for some utility) then you can start getting
utility from your flying about 4 months or so into the game.

If you actually want to be insured (even for liability only) then the
first year of jet ownership will probably mean having an instructor
pilot in the jet in any case - nobody will write you any other way, if
at all.

Michael