This is a legitimate concern. I remember running the NYC marathon and being told that my bib # had to be visible at all times for the course camera. Since I started the race with several layers on, I put on a long sleeve shirt covered by a short sleeve short with the bib on it covered by a jacket that I left open so the bib would show. I tossed the jacket early in the race. Around mile 8 when I wanted to take off a layer, I actually stripped off both shirts (wearing an appropriate running bra underneath, of course), tied the long sleeve shirt around my waist, and put the short sleeve one with the bib back on. Sounds complicated but only took a few seconds and I could do it while running.
I'm not sure if Disney has as strict rules about your bib showing at all times, but when I ran there, it was hot enough not to need a jacket so that wasn't an issue. I doubt your 5K tomorrow has such strict rules about the bib showing. I'd wear long sleeves tomorrow with the bib on it, be chilly before the race begins, and then be warm enough while you're racing. Or else you could pin it on your waist like some people do, and then it wouldn't matter about the jacket.