There is generally a misconception about what qualifies you for recurrent training or initial for that matter on a BBJ. Generally speaking 121 training does not simply transfer over to most of the BBJ's. If the BBJ is on a Part 135 certificate, then you need a Part 135 checkride. If the aircraft is on a Part 125 certificate, then you need a Part 125 checkride. Part 125 does not require any training, only checking...but most 125 operators have a training plan built into their certifcate and thus there in fact is training under the conditions of that certificate. I know of several 121 guys who are doing contract work on a 757 Part 125 operation and they all need some amount of ground/FTD training plus a Part 125 checkride using the operators procedures.
There is propsed Part 125 language that would recognize Part 121 for Part 125 ops but it has yet to be approved.
For the really low ball BBJ operators they can go out and get someone like Higher Power to do two day recurrent sim and a check ride and requal a pilot who has not been in the B737 for 7+ years. Obviously they have a sweet heart deal with their POI. Fooking amazing.