All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
The game of bowling is defined as a sport involving rolling a ball to knock down wooden pins with the aim of scoring points. According to the general rule in Sharia, this sport is permissible, as it relies on physical and mental skills.
Generally speaking, the general rule for engaging in sports is permissibility, provided that any potential violations of Islamic principles are avoided. These may include exposing the 'Awrah (parts of the body that must be covered), intentionally harming oneself or the opponent, engaging in financial gambling, being distracted from performing religious obligations and duties, or participating in prohibited mixing between genders during the activity, and similar matters.
Engaging in sports is among the activities encouraged in Islam, especially those with significant value in enhancing physical fitness and promoting good health. This is based on the saying of the Prophet Muhammad (PBUH): "The strong believer is better and more beloved to Allah than the weak believer, while there is good in both." [Moslim].
In conclusion, the ruling on bowling is permissibility, provided it is free from the aforementioned Sharia prohibitions. And Allah The Almighty Knows Best.