I hope this answer is not too late in your search for a billing company. I am a health club owner as well as a software developer who started my own health club software systems. My systems include both a gym management system and a billing online service all in one. I have free trials if you want to look into it. Also, after developing these systems, my club virtually (literally) runs itself. I only have one other staff member.
If you have a chance to explore the free trial to see if it is for you, please let me know what you think.
Insight is the GMS: http://www.gyminsight.com/
If you want any other gym business insights, please visit my blog at: http://blog.gyminsight.com/blog