I am sure that you can bring your own equipment if you don't mind carrying the extra weight with you.
When we bowled the ship was very steady and there were flat seas. Therefore, there was no effect on the bowling performance. I am sure that in high seas, there could be some problems.
Note: when the ship is in port, they usually reduce the price by 50%. There are usually very few people partaking unless it is rainging outside. We bowled a few games one afternoon and the attendant actually told us to bowl another set for free.