Here is my guess. First, I think you are talking about the character flickering onto the display very briefly before it really appears properly in the scene. If not, the following is not useful!
With things like hair and dangles, what can happen at the start of a scene with draggers is it has a frame or two of trying to get in sync. So you can get weird hair flying at weird angles, or just gravity taking a few seconds to settle down (the hair will drop due to gravity until it finds a steady point between the head it is attached to and gravity pulling it down). The only way I know to fix this at present is to render the scene to a video file, then trim off the start and end of the video clip in premier pro. If you trim the scene in Character Animator it does not fix it - it still has to settle down.
A similar thing is happening with hands for some puppets. If you drag, the hands point their default way, ignoring the drag of the arm (so they point the wrong way with respect to the rest of the arm). Again, trimming is the only solution I know of.
In your case, my bet is you are using a dragger to position the bee. So the default X,Y position is in scene, but you drag it out of scene (or to a different location in the scene) and start recording. However there is a lag as it jumps to the dragger location (Ch does all sorts of blend etc magic), so I think you need to do one of two things.
(1) Render to a video file and use Premier Pro or similar to splice out those unwanted frames.
(2) Start with the puppet X/Y position being exactly where it should start from, then drag relative to that start point - so there is no laggy jump. (That might work for your case, but does not solve the other cases I talked about above.)
I created a feature request to be able to control the number of frames to skip at start of scene to allow gravity etc to settle down. Its like “okay, you have to do your stuff, and if its falling leaves/snow it will never reach a steady state” but at least give the creator a chance to determine how long before the stead state starts, so they can trim off these bits inside Character Animator. Its a little annoying to be forced to render to a video and manually trim it. It slows down the workflow of creating. I want it to remember such changes.