Some schools will accept you if you don't have a Bachelor degree BUT only on the proviso you hold a TESOL certificate or equivalent. Other schools will pay you more if you hold a TESOL AND a Bachelor degree.
When schools make mention they require a teaching certificate, they are mostly referring to TESOL, TEFL, TESL etc. One of these certificates on it's own will only scrape you across the line to getting a teaching job. You will need to go through the numbers in applying before being accepted.
I have never heard of Teach International. I suggest sticking to the mainstream schools that have been around a while. Just take a look at
www.aacircle.com.au/tesl_tefl.htm.