I stand (somewhat) corrected.
Under §14 CFR 61.157 you can't go from nothing to an ATP on the FAA system without holding a foreign licence as described. You could however get a Commercial as a stepping stone and then do an ATP later, penalty would fundamentally be an extra written test.
If you go straight to an ATP, you need the confirmation of your foreign licence as previously discussed, sorry, my bad on that one.
For private ops a Commercial is fine for PIC of a part 25 aircraft, given that you have a non FAA ATPL you can probably beat any insurance stipulation too.
@VJW Exactly which part under which you'd operate a BBJ (121 or 135) commercially I suppose just depends on the certificate holder. Which written you did and how you originally applied the type to your certificate is not however a bar to doing a check ride to do operations under any different part. As NuName said, and I was eluding to earlier, the work permit issue is more than likely to be your big man rather than anything you might find in the depths of article 14.