Another way to get bikes is to partner with local commercial bike shops. Sometimes when someone buys a new bike they ask if there is a place where they can donate their old one. A nice shop will either direct such customers to your facility, or collect used bikes on your behalf and phone you when it's time for you to pick them up.
Your donations website should clearly describe any limits you wish to place upon the types of bikes that you accept. For example, your shop may not want to accept bikes that have been stored outside and have turned into rusty lumps; however, a rusty chain is no problem. Other shops may choose not to accept cheap department store bikes as donations, if they already have a steady stream of more decent bikes.
On the other hand, in my experience, it's asking too much to expect a random donor to be able to evaluate the quality and condition of the bikes they wish to donate. If you can handle it, it might be best to accept all bike donations, take off any useful parts, and recycle or give away whatever you can't use.
Gordon