Ask yourself, "What am I going to use this room for"? Will I be mostly playing by myself, have buddies over, your kids and their friends playing, part of a total entertainment room, etc.? If it's for yourself 16 by 20 is the bare minimum. If part of an entertainment room with a bar...I guess you get the picture.
One more consideration, height of the ceiling. Why? Because good table lighting is important and lights can be recessed or hanging. After you bang your head or cue on the light a few times, you will soon see the mistake. A higher ceiling will improve air control.
Any quality builder will suggest using a steel beam in the ceiling to give you a large enough room without poles. It will not add much expense if included in the original plans.
Another thought: windows and doors. Outside light is not conducive to optimal playing conditions and the possibility of balls hitting the glass will remind you of Murphy's Law. Good blinds or curtains may minimize this. If smoking is considered, a door outside to a patio smoking area will help.
It is usually more pleasant to play pool in a cooler room, so I suggest it be on a lower level of the house instead of the bonus room. And a fireplace by the bar may look great but may not be practicable.
Flooring? My floor is concrete with carpet over it. For three reasons: to deaden the sound, it's more comfortable, and it will keep the table more level than a wood floor. Believe me, a loud pool room in the house can make it very unpleasant for the rest of the family. To reduce noise, insulating the pool room walls will help keep ball banging noise escaping to the rest of the house.
If you are going to put a TV or sound system in, plan for it now. If a bar is an option, you may need water and sewer. And that leads to my final comment, if many people will use this room, close access to a restroom instead path trough the house is practicable.
When I built my home, I planned for two bedrooms and a full bath connected to the entertainment room. If I or my kids had friends over, it was much more convenient.