We've consulted with psychs, counselors, and our children have been through multiple therapies. I'll echo DeeDee's advice to look for a local children's hospital - ours has always been cooperative and helpful in billing insurance directly. Other private providers typically don't bill insurance (although our neuropsychologist does). *However* - that doesn't mean our insurance didn't cover the services, it just meant the provider wouldn't bill directly for us, and we had to submit the paperwork directly to our insurance company after the services were given. There were cases where our insurance company covered a certain type of service but said (in the policy) that we had to go through a preferred provider (this particularly occurred on our behavioral insurance policy), but we were able to have out-of-network providers after we'd written in and called the insurance company and explained what services we needed and why we needed to go out of network. And there were also services they simply didn't cover... but overall, if it was a service that the insurance company intended to be covered we were usually able to work something out so that insurance paid for it.
I'll also add that we've never worked with providers (either psychs or therapists) who specialize or have a ton of experience working with gifted children - we're in an area where there really aren't providers with a lot of that type of experience. We've had really good experiences in spite of that! The providers that have been the most helpful to our children are professionals who are really interested in our children, who like working with outside-the-box challenges or simply something different than what they usually see, they are able to develop a rapport with our kids, and most of all, are invested in helping our kids. IF we had the choice, sure, we'd like to consult with professionals who have expertise or who specialize in working with gifted children. We didn't have that choice, and it's been ok anyway - so don't give up!
Best wishes,
polarbear