It sounds like you're describing freelancing, rather than contracting.
Contracting is basically a full time job, but you own the company, can claim expenses / equipment / etc, and otherwise, it works like a normal paid job. You dont, EVER, bid on jobs, you get hired for a set period. Companies like this as it's an _operational_ expense not a HR expense, and chances are, they have a hiring freeze :)
If you already have clients lined up where you can do work as or within a company without first freelancing, then you're probably not in HN asking how to do it.
Edit: also, many of the other comments here were, get a client, not speak to a recruiter, so this was somewhat a response to that add well.
In the UK, permanent salaries are very low compared to other english speaking markets. Several people (self included) mentioned contracting. This is distinct from freelancing in that it usually for a company running a project but in need of some specific skills for a fixed time at a daily rate, rather than asking you to make something for a fixed price.
I see them as distinct career paths, and I'm pretty sure the question was aimed at this.
I'm getting the feeling that rather like employees who've never considered going independent, there are quite a few people posting here who work as contractors in the sense you're describing (which I'm not saying is incorrect, just incomplete) and don't realise that there is a wider world where maybe other contractors don't work the same way.