What is competitor billing?

Basically, its as it says - A bill from a competitor that is offering a similar service.

The idea is that your previous (or current) provider has already checked your credentials (proof of income etc), and has given them the all clear - otherwise they wouldn't have accepted you in the first place.

So, based on the assumption that everything is in order, your potential new provider will not have to run extensive checks on you themselves, as your old/current one already has.