The criteria to get someone to outsource business to you varies case-by-case. I can answer to you from the translation outsourcing point of view. I believe these criteria can be applied also to other kinds of outsourcing.
* Credibility is very important so that you client can trust you (references from existing customers are excellent way to improve credibility)
* Price-quality -ratio must be good so that your client gets values for his/her money
* Contract is very important: you have to clearly commit to what you are selling. Both parties must know what to expect from each other.
I think these are the most important but as I said, the criteria varies a lot. You can also think what you yourself would require if you were to outsource your business to someone else.