What happens if you place an electric coil around a rod of Bismuth?

It would just get hot, I suppose. You can quite easily melt it and make pretty looking crystallised blocks of the stuff. Here’s a good Instructable: http://www.instructables.com/id/Fun-with-Bismuth/

If it melts on your electrical coil, it might make a bit of a mess of it, but they say it doesn’t stick to other metals very well, so it can just be scraped off.

You have made a bismuth core inductor. Provided it does not warm up it will reduce the inductance slightly over an air core inductor because of the magnetic permeability. Normally cores are used to increase the inductance but bismuth is diamagnetic.

are you using it to electroplate or something?