A-bus,
Yes, you may act as an FO on any business jet without a type ratign. You'll probably attend an SIC initial at an approved training provider. I don't have my reg book handy but I believe FAR 61.55 covers this area.
Now, the caveat. ICAO requires that both pilot's be type rated. In short this means that any international work you do, you will have to hold a type rating. There are some flight departments that still use non-typed FO's on international flights but many ICAO countries are cracking down during ramp checks. From what I've been reading lately, this is especially true in France. Those who don't use two type rated pilot's run the risk of a grounded aircraft if ramp checked until a second typed pilot can be brought in.
JAA SAFA (Safety Assessment of Foreign Aircraft) is running more inspections from what I've been reading lately. Anyone operating within an ECAC (JAA) country is subject to receiving a random inspection. It doesn't matter if you are from an ECAC (European Civil Aviation Conference) member nation, non-ECAC nation, Part 91,135,121, etc. NBAA's message board is having a great debate on this very subject of late.
Side note: ICAO also has a rule against those pilot's, both captain's and FO's (typed) who are over age 60 from operating in their airspace!
Again, the FAA does not require you to hold a type rating to act as an FO on business aircraft.
2000Flyer