After reading your post, the first thing I thought of was something like the following, having seen them on TV.

Kicpot Hands-free Reusable Shoe Covers, Step on Heavy PU Coating Easy to Wipe Indoor Outdoor Work Boot Covers - Perfect for Home Workers 17.311.8inch (1 Pair) (Blue) https://www.amazon.com/dp/B07CVJH8NX/ref=cm_sw_r_cp_apa_i_Br0pEbQHDZE72

Not the greatest of reviews, but intriguing. Wonder if they would hold up for occasional use at the lanes. I rarely wander away during bowling, so having something easy on, easy off might be worth taking a chance on.