Yeah, you may be right. I just haven't noticed it at all flying smaller, twin engines planes. I have flown the bigger commercial jets (747, 787, A320, and the 737 a few times and didn't noticed it on them as well. So I was surprised when I experienced the bobbing on the 146. My last flight with the new PMDG 737 was absolutely smooth. Every flight I've taken with the BAE 146 bobbed away at level flight using AP. I did think to myself if it could be related to the trim on the 146.
Perhaps, I've missed a detail/setting in preparing the plane for flying that may be contributing to this. I'm still in the mode of simply jumping into the plane and taking off. I'm starting to get more technical with certain checklist, but I'm not there yet. It's easier to do with a little C-172.
I was looking through the 146 manual last night and did notice, the AP buttons, submodes, etc, seem to be a bit more involved than with the smaller planes(not suprising). So, I still have much to learn. I do almost exclusively, use the MSFS Mobile Companion App to help me set up some of the basic AP controls rather than using the instrument panel. It's a great little app in that regard.
Anyway, I'll continue to read, watch and experiment to further my knowledge of the 146.
Ona a side note... Back in the late 80's doing consulting work, I got to fly on a lot of planes(understatement), and many times it was a BAE 146. I wasn't into siming at the time, but always enjoyed the ride in the 146. It's a cool little 4-engine jet. So when I heard Just Flight was releasing it, I knew it would end up in my hanger! :)