Cobar to Kamillaroi - shortcuts?

I really don't know why you want to cut out Bourke, it is probably the shortest and quickets way, all bitumen.
But if you really want to bypass it, continue onto Nyngan, down the Mitchell to Nevertire, turn left along the Oxley (17km) to Warren, from Warren to Coonamble, onto Walgett, then Collarenabri then Moree.

From memory it is all bitumen between Warren and Coonamble, much of it is single lane bitumen but a good road. There is a fractionally shorter but much rougher road between Nyngan & Warren, not worth it.
I can't remember if it is all bitiumen between Collarnabri and Walgett, probably is. I'm normally on side roads through there.
There are a myriad of variations you could do including Coonamble to Narrabri through Pilliga. You can also go via Macquarie Marshes & Carinda on dirt roads and single lane bitumen directly from Nyngan to Walgett, with a multitude of T intersections and various turns. You want to have good maps for that, I occasionally find the road signs have been turned around "for fun" by people through there.

Depending on when you are going with good rain forecast late this week, I wouldn't plan on travelling on any of those grey clay dirt roads from this Thursday for a week.