Hi whistle. Glad to hear that you are looking for a new job. I know that it sounds strange to say this but so many people have a really hard time in private schools are over the world and still stay there and take it. I stand for absolutely no crap. I am a complete ******* to the bosses but great to the kids. I care only about the kids and know that the bosses can't just get rid of me as 1) they would have to find a new teacher to replace me and 2) I have experience which a lot of teachers don't actually have, especially the ones fresh out of college and they know that I know that. I get paid weekly or fortnightly from all my jobs instead of the usual monthly.
Well what I am trying to say is that you should try and do some part time jobs if you don't want to commit fully. The pay is a lot better and it can be refreshing as you could have 4 different schools a week (like me) so you don't have to deal with the same old bad students who is always causing trouble in your second class who will be unnamed!
I advise getting a reference from your current school. Look around for some jobs but don't send your resume or number as they are like dogs sometimes with their frequent calling, until you are sure about the job. Always have an interview and check the place beforehand and never, never let the agency get money from your salary as they already get paid from the schools looking for you!
And never be easy. They want you, not the other way around.