I think we may not quite mean the same thing when talking about a charter company. By charter company I mean one of the airlines that works for travel agents and holiday tour operators, for example Britannia / Thomsonfly, First Choice, Excel, MyTravel and Monarch. Most of these companies fly less in the Winter, hence I have time to work on my other part-time consultancy work in the Winter.
As for contracts on Citations and biz-jets - I have no knowledge of that side of the industry so I do not know what their standard terms and conditions are.
However I can say that there are plenty of contracts, short and longer term, on Boeings and Airbuses if you are prepared to work anywhere worldwide. The Far East and Eastern Europe both seem to have a boom in opportunities for contract pilots at the moment. I do not know what the implications would be for line training and line checks. However, most contract opportunities state that applicants must be current on type and have a min of about 500 hrs on type - therefore there is no real chance of contracting straight out of flight school. You'll need another airline job to build that experience first.