Using an out of network midwife at Alta Bates

Hi! I’m hoping to get some information about the full cost of using a private practice midwife at Alta Bates. I have Blue Cross PPO which in network with Alta Bates, but would like to use a private practice midwife in Berkeley who will charge a flat fee for her services, and has privileges to deliver at AB. I know her cost and what percentage my insurance will cover with my out of network benefits, but I’m trying to get a clearer sense of the hospital costs. Were you charged just a “facilities fee” for using the hospital, or did you end up getting charged a provider fee as well? I’d love to have a ballpark sense of what it all cost— am I looking at a ~5k birth here or ~10k? Can anyone speak to their experience? Thanks!