Trying to recreate a game intended to be played on a flat surface in a gravity well whilst in a microgravity chamber seems not only futile, but it also passes up an opportunity to create a new game that makes better use of the features of the environment that hinder conventional bowling.
My suggestion: orbit bowling.
Set up the court by placing the target (call it a sun or planet or black hole; whatever takes your fancy). This object floats in space and is given a generous electrostatic charge by a small van de Graaf generator ahead of time. Collision of the target with a wall or other non-game object ends the round, and may involve a forfeit for the placer. The setup therefore requires a little skill (because perfectly stationary placement may be impractical), and players take turns setting up the court for each round.
The objective of the game is to throw your bowls such that they enter into an electrostatic orbit around the target for a) a certain amount of time (the length of a round, probably quite short) and b) that has a lower periapsis than all your opponent's bowls (alternate rules might require circular orbits or at least ones of limited eccentricity, but that sounds dull). Bowls that crash onto the target and stick are non-scoring. Such a move might be considered a round-losing foul under some rules, but that seems like it would discourage risky play and make the game a little less interesting.
Your bowls are made of a suitable lightweight material (perhaps expanded polystrene foam? heavy bowls would be better, of course, but you start running into safety issues involving field strengths and dielectric breakdown...) and are suitably charged before the throw by an appropriate means (rubbing them on a foam sheet sounds like a reasonable method, but maybe you could have a little van de Graaf of your own). You may charge your bowls with the polarity of your choice, but to win you'll need at least one that is attracted to the target. Like-charged bowls won't orbit the target, but may be a good means of disrupting your opponent's bowls without having to hit them directly.
This game maintains the basic goals of bowling-type games, whilst giving them a new and uniquely space-oriented theme. In a suitable fictional setting, it might also help practise certain kinds of orbital mechanics...
Relevant video: https://www.youtube.com/watch?v=m0Ei6h3LVb0 at about 3:50
He cheats a little by moving the target slightly to stop the orbit decaying. You might perhaps be able to take a leaf out of the book of curling and make it a team game where one player bowls and the other player (or players) on their team have limited means to shepherd the projectile and help inject it into a more stable orbit.