I have some thoughts on this. I got my GC license a couple years ago so I could build houses myself as I was sick of dealing with contractors.
I've hired plenty of contractors that were not licensed/insured and it went fine. I think there is a common misunderstanding that licensed contractors cost more. Not exactly. Licensed contractors have more of their "shtuff" together and thus are better at their job and naturally will cost more. The license doesn't cost more, the service and quality does.
And a note on that cost, in my experience hiring contractors, only a small percentage of the cost savings was due to finding the right guy who is willing to work for less. Every time, most of the cost difference was quality. I had an electrician run wires in an attic, telling me up front that the house won't be up to codes, he's only doing the one or two things I asked. Little did I know even on the brand new wires he was running, he was twisting them together with no junction box! This guy wasn't any cheaper. He was more expensive because now I gotta pay someone else to fix it.
But here's the other side of the license issue. It's very cheap and not difficult to maintain bond/license/insurance. So if this guy doesn't have them, it's a bit surprising. If he's only doing bathroom remodels, that would make sense to not bother. But anyone who considers themselves a GC for hire, it's a bit odd they wouldn't first get their ducks in a row, it's quite easy.
If it was me, I wouldn't worry about him not being licensed/insured, I would just make sure to vet him. Talk to other clients, go look at his current job site and see how clean it is, the quality of work, if the order of operations is making sense so far, etc.
PS I'm a GC in the Nashville area and can take on a handful of clients in 2025 if you need me.