You don't have to make the bar any more rigid than your tool post and compound. At ten inches out, if nothing else (and there's probably something else...), that bolt in your tool post is going to start to feel a little lonely there all by it's self. You're going to have to manage the cutting forces pretty closely no matter how rigid the bar is. So yes, fancy steel in huge diameters is technically a lot more rigid, but at some point it's just not going to buy you anything extra.
I'm gonna jump on the 3/4 mild steel bandwagon, (or bigger is fine if that's what you've got), and save the "good stuff" for something that warrants it. And I'm going to say that even if you bought the most expensive carbide boring bar you could find, you're STILL going to want to get at least a couple of cuts in to work out the deflection before you start approaching a final dimension.
