There are a lot of solutions out there that tackle billing but they may not necessarily be open source. Examples being chargify [0], recurly [1] etc.
A couple of open source solutions that I found are killbill[2], laravel spark [3], bullettrain [4], opensourcebilling [5]. Again, they may not necessarily be 100% free but they are open source.
Also, billing is a very subjective term. Do you mean subscription billing or just plain old invoice type solutions or a combination ? There are tons of invoicing tools like invoiceninja [6] and plenty others.
[3] https://spark.laravel.com (billing plus SAAS)
[4] https://bullettrain.co (billing plus SAAS)