Best way to "prove yourself" without any sort of degree is to get TEFL certified. There are several good ones (I went through i-to-i to get mine) out there, but I didn't get it because I needed it, I went through the course so I would have "paper proof" that I knew what I was doing.
Do you need to know what you're doing in China to get a job? Absolutely not, however, no experience at all teaching or being in a classroom setting can be REALLY frustrating especially if they stick you with a class who has a very low English level to begin with. I've seen foreigners come and go rather quickly just because of the frustration factor in the classroom alone - but then add in all the other stressors of going abroad and they soon find reason to leave, change schools, or react in all sorts of ways that leave the Chinese rather dumbfounded.
Chinese colleges and universities do require a BA degree, and this only makes sense form an educational point of view. Who wants to be taught in a college by someone who never graduated from one?
That said, there are many businesses that have set themsevles up as crash schools where no degree is necessary, but definitely a plus. Then there is the possibilty of teaching in middle schools and primary schools where the requirements are definitely lower.
Best way to prove yourself is get that TEFL Certificate and two years of experience. By then your options should really open up, and you'll have a better sense of what life in China is like and what is available.
A word of warning - be careful in your school selection. Ask for the contract up front, research the school online (check blacklists here and at BuXiBan.com) and ask the school you want to teach at for the e-mail addresses of other teachers who have worked there before. Minimum 5 and preferably 10 is the rule of thumb here.
I also have a list of "Negotiating points" to make sure are included in any contract, as well as a sample contract where most of those points were added in by myself. There is another very good website with very good advice concerning scams and contracts at
http://www.bearcanada.com/eslmain.html