I wouldn't skimp on two things in bonsai: wire and tree material. Wire and tree material and tools, (okay, three things)are essential to enjoying this art. It's difficult to replace any of the three.

This actually works very well. Professionally made bonsai wire is a joy to work with, but bhen I was very low on cash, I took a propane torch to coils of various sized leftover electrical wire. With a torch you can be sure to get it all red hot, and use less fuel (and time) than a grill would- unless you're just dropping it into coals while you wait for an ash layer on them. Putting it in the hottest coals of a fireplace works too; also making few coils into the same size as the ring of flame on a gas cooking stove (but its harder to get it all in the flames just right).

Electrical wire is about the purest copper wire, and usually less expensive per length than bare wire bought in smaller coils from a hardware store.

I used common 12 & 14 gauge stripped electrical wire, leftovers from house wiring, and just bought a few coils of smaller sizes. I also used solid copper bell wire scrap a few times, but it was hardly worth the effort of stripping (I don't burn it off because of the pollution that causes). Not usually much point in wiring branches that small anyway, where weights can work better.

You can also recycle the wire a couple times by straightening it and re-annealing. It doesn't work indefinitely though, and the work involved makes it hard to justify the little money saved. I mostly just took my used stuff to a metal shop that had recycling bins.