The main bus service by a mile is Surfside busline, their website is at http://www.surfside.com.au/ and in fact if I can recall back far enough they were given a monopoly and heavy subsidies after a few hitch hikers were murdered back in the 70's or 80's.
They run a pretty good service to and from the main theme parks and Broadbeach is a main link point. I'm pretty sure they will have a timetable and info about day passes etc on the website.
Your accommodation will also be able to advise if shuttles can get you to and from theme parks, and the cost too I would think.
Overall Surfside will give you all you want. Cheerz Wab.