You can always do a 30 day search using ITA/Matrix and the faring option of F BC=I (only the cheapest fare class for the bundled business class). Or a similar fare class search for a "bundled" economy ticket.
It is my understanding that ITA/Matrix searches do not use a real time copy of the GDS so you will have to do a verification booking using an OTA or the QR website to verify the fare availability.