Hi Peyton, maybe it would help if you tell us which DAW you are using for your production, but for instance, I normally use Sony Acid Pro, and what I do specially if there is a midi part involved, is to make sure i set the DAW tempo to the same one that of the original BIB created song, that way the beat markers are the same and all your wav files and midi should line up. Usually the count in is four beats, so you place all your files four beats to the right from the beginning. I'm assuming that the same principle works for most DAWs ( I'm not an expert in this matters) my suggestion is based on my own experience. As far as copying an pasting a part, having the beats at the same place would also help, so all you need to pay attention to is at what bar on BIB the part you want to copy is at so you can paste your copy at the correct place so the chord are correct.
Maybe someone more experienced in this forum can correct me if I'm wrong or make a better or easier suggestion. I hope this help.