No doubt, that there is a large span of operators within the Biz Jet sector - as is there in the Airline industry. Airline flying is what airline flying is - that boils down to ones personal liking, but the slave contracts and ****ty pay is as bad within the airline part of the industry - though you'd probably have a know roster that's better than your current situation..
I don't quite see why any airline would not find a biz jet pilot with 6000tt interesting as from an pure time and background wise point. Which airlines would dislike this?