Finding Work in Busan is Hard?

It is getting more difficult as a lot of private instituitions are struggling with economic issues and the public schools are cutting back on hiring too. This has lead to a lot of people battling for the same jobs however if you keep trying I'm sure you will get something. Having your documents already prepared is a big plus. My advice is usually stay clear of recruiters as they all have the same jobs available and it's usually the ones no one else wants.

Personally I feel it's best to consider other places in Korea. Ulsan is a 40 minute bus ride to Busan. There's heaps of work here. 

A previous comment about the economy is true in most places in Korea. Be patient, something will turn up.

Look here on Korean Bridge for jobs, also on waygook.org. The best way is to join Busan facebook groups and look for people who say their Hagwon is hiring.

Like someone else mentioned, joining a Busan group on facebook is a good idea. Alot of people will post there when their school is looking to hire. 

You might not always have the the choice to avoid recruiters. When you're in contact with them, I think it's important to be persistant. They sometimes have a hard time selling the cities that aren't Busan or Seoul and are quick to tell someone there are no jobs in a place so that they might be able to persuade them to go elsewhere. Decide where you want to be and let them know that. If you have the time, and can be patient, you can wait it out a while to see what the situation is before you decide to start trying for another city. Like another poster said, there are a few cities that are close enough to Busan. 

You will hear the same things from recruiters in Seoul, ie preferably North American Female but it's not exactly the truth. Don't be discouraged by that bullsh*t. You have only been job-searching for two weeks, relax, it will take longer than that in Seoul or Busan because of the amount of people applying versus the amount of jobs. It's definitely  true that there are fewer jobs because of  the economy, teachers staying for longer, less public school jobs etc but if you really want to come to Busan don't give up yet. 

I'm not sure why you expect to find a job in your prefered area so quickly.  I've gone through a few jobs over the years, and even with a masters, experience, and being in country, jobs don't jump up the instant you want them.  I've known a couple of female Americans in Korea with good social networks who've had to look for more than a couple of weeks to find something.

You're neither unlucky nor too ambitious, but you are unrealistically impatient.