Not sure why this happened, but I felt it should be documented due to how weird it was.
Basically, I was bowling my third bowl in the last frame (due to getting a strike), and when the dialogue to add spin appeared, the ball completely disappeared from my character. Then, when the ball was meant to start rolling, my player (minus accessories) disappeared entirely, but neither the camera nor ball moved at all. This lasted until I pressed left click (opening the Esc menu or chat did nothing), where the ball then rolled normally.