There are many alternatives to host bill. I think you should sit down take a hour or two out of your time and play with all the different options you have here.
There's whmcs most used today on most hosts it is very easy to set up and configure even easier to customize the looks of it or even intergrade it with your website.
Clientexec is a little old but the new version coming out looks pretty sick and dope.
Hostbillapp is nice but it can be a bit pricy for certain people .
Blesta is new and very cheap and affordable for most business owners it's basic and just gets the job done z
As for free and open source what not there's phpcoin script looks very outdated and looks like it's from the 1990s but it gets the job done and is easy to set up and especially customize up enhance it with simple php coding