Out of a principle of no government interference in the free market... or because these are Southern Senators, whose states host foreign-owned auto plants with no unions and lower pay?

Both, I'd guess. The bailout is a really bad idea: it's a subsidization of an incredibly uncompetitive industry, which will leave it just as uncompetitive as before. If you want to see where that leads, look at some of the British industries in the 1970's, before Thatcher's reforms.

The auto-bailout is a bad idea. We tried to save our wharf industry in the 1970's by this sort of government interference. It had two predictable results: It cost a lot of money and it didn't work anyway. (No wharf industry of note survived)

It is much better to put the aid in restructuring. Give people loans for reeducation, provide general National Bank loans (since the normal banks likely don't offer any) for newly started enterprises and select old ones with credibility, and put funds into research, infrastructure and education improvement. Or, worst case, relocation.

That said, I don't understand why the unions live under a system where foreign manufacturers don't have to sign union deals. It seems short-sighted of the UAW or whatever they're called to even allow that without labour conflict. If a foreign manufacturer was trying to do that here I'd expect strikes and blockades.

Well, I think it is reasonable to expect that corps in countries without general welfare systems who thus would have to pay "extra" welfare for unionized and skilled labor capable of making such demands would have a competitive drawback against corps who already operate under a national welfare system - but on the other hand this should also be balanced by lower taxes and such. I'll note that the pay in the article noted as GM average - 28USD per hour - would make for a quite good income in my country. 25 USD per hour, the Nissan standard, wouldn't be bad either. And I assume that's before tax, which would amplify differences even more. Nissan doesn't seem to underpay people to me, it seems as GM & gang has been too cozy with the unions for the financial long-term good.

Blockades. Well...
Around here the national unions call out blockades anyway. Individual workers don't have to be union - but the corporation must accept unions. We had a wonderful example of some sort of cafeteria in Gothenburg where the owner refused to sign union deals and the staff all were perfectly happy without being union. Unsurpringly, the Trade Workers Union called out for blockade and the entire rest of the Union conglomerate followed suit. No one handles the deliveries, no one picks up the trash, picketing all day... ...course, the owner had to give up. (And sell the cafeteria)