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The sexy way to implement this (horrible) idea is to have a smoke/fog curtain at the end of the lane, and project onto the fog. The ball could slide through silently, and then the synthetic image (and sound!) would be cued.
Maybe there's a big sheet of glass suspended at an angle around the last quarter of the lane. The ball rolls under the glass into darkness and is visually replaced seamlessly by the virtual ball shown on a screen hanging on the ceiling, facing away from the bowlers- a Pepper's Ghost effect.
The first issue with this of course is that it would only work from certain angles; the possibly larger issue is that you'd have people rolling bowling balls at a giant sheet of glass.
The focus is golf, but they do have a bowling mode where you throw the ball and the camera picks it up and simulates it on the projector. It's not attempting to replace the bowling alley in town though.
Here's an idea: instead of requiring the whole 60ft lane, just have a lane ~10 ft long with a trap at the end. Based on the measured spin, angle etc, you could project the trajectory down the virtual lane.
Use one of those head-tracking techs (Dimenco screens?)
This would allow you to have like 3x-4x the number of bowling lanes in the same building footprint.