There is not much difference between bleach and so called home mold inspection contractors.
I would not recommend using bleach to clean mold, in fact it will not kill the DNA makeup of the mold. So in about a week you will find it coming back.
There are mold products that you can spray in the A/C that will change the DNA makeup of mold. There is some mold kits out there like Molderizer and Safe Shield, but I believe finding the source it truly the main issue you need to handle before even think of buying a product.
I would see if you have any moisture around the A/C, this may be from the system needing a balance. I find mold problems caused from a leaky A/C handler.
Look if you keep getting no where, you could always do it yourself and remove the mold problem yourself, this video on youtube
shows all the equipment and procedures you would need.