Don't do it before you got your CMD in the A320 and plenty of hours PIC. Even then, consider the move very carefully.
Business Aviation can be the job of your dream on a fancy Global Express or Gulfstream and takes you to the most beautiful places, 5 star hotels and on top of that a great salary...
Reality for most Bizav pilots is the exact opposite. Most fly on smaller jets such as Citations, Embraer Phenom, King Air, etc and barely make a living from that. Lots of freelancers that compete for days and drive down the daily rates. Most smaller outfits are too small to participate with the bigger charter companies and it's a race to the bottom condition and even safetywise.
Plus - without any offense - many Airline pilots that flew Boeings or Airbusses before assume, that this experience will lead to immediate Gulfstream, Global Express or Falcon epmployment or even BBJ/ACJ jobs. The reality could be that these guys need to work their way up starting on a smaller jet, possibly with self paid training.
If you really consider it, I would try to go part time with your current job (if that's even possible), try some networking or even consider to buy a cheap typerating (King Air, Cessna Citation, XLS, etc) to get started. Knock on a few doors and get a foot into the world of Business Aviation.
Needless to say that you might have to book your own hotels, arrange transportation, arrange maintenance enroute (oil, oxygen, tire svc), print (or even plan) your flightplans, pay handling fees, arrange fueling, arrange permits, arrange (or buy or even create) catering, buy magazines/newspapers/flowers/alcohol/toys,whatever... for VIP clients, download and install NAV updates on board, update and charge iPads, do online training while in the hotel - and that all is done before you even get to fly the thing... Imagine that with a fresh CPL graduate doing his first rotation with you, with a very demanding client on board, marginal weather into funny planes such as Samedan, Cannes, Sion or Chambery (where you have never been before)... and don't forget the broker who calls you every 15 minutes to ask you if the aircraft is ready
And that you do on every day while on duty for 7-15 days in a row for less pay than you make with your current job.
cheers