What I've done in the past is call the offending motorist's insurance company, inform them calmly that I'm filing a claim, and tell them (not ask) that I'll be billing them for a rental. That has worked very well for me.

I had one threaten to refuse the rental. "No problem," I said. "You can pay for the rental, for my time to fight this, and my attorney's fees. Unless there's anything else, I need to call my lawyer now." They backed down and paid the rental.