Got Indy to help me investigate. He mentioned his DM enter tool didn't work on the transition, but he could cross it without bouncing.
I even managed a triple bounce sometimes: I enter, get bounced a first time when I arrive on the bridge map, get bounced _again_ on the regular Mist tile, get bounced a second time on the bridge map, and finally land back on the original map.
The whole load sequence means that if I don't move after landing, my textures don't load and I am truly invisible.

Not sure if that's related to anything, could just be a side-effect, but I don't know.