You can control when and how everything is printed through rules and actions. look through your rules and find Print Bill action. Study it and then you can pretty much tell it to print or not to print whenever you want.
Its hard for us to just give you a solution. Everyone has different needs.
It sounds like yours is set to print on ticket close. You could change it to payment processed. Or if you want both you would need to use an Ask Question Action. If you are interested in Ask Question Action there are great tutorials under Tutorials category of this forum.