When I say "network" think less LinkedIn and more people you've built up enough trust with to swap phone numbers and keep each other informed of opportunities, provide references etc.
"Hi XYZ... I've started consulting, and I'm looking for new business opportunities. I'd love to talk to you about this... could we catch up over a call sometime next week"
may be there is a better way to do that. I've limited 1st degree network, and I don't want to burn it all, so I stopped sending these messages after all the first 4-5 didn't seem to go as planned!