Earlier quoted context omitted.
No. The right way is to issue 50B of stock back to the public. The shareholders who received 50B and are holding it in their personal emergency funds can buy it back, or new investors can. There's more than enough private capital available without requiring the government to step in.
The public currently wouldn't buy the stock due to bankruptcy risk. If the government commits to buying what's left at the same terms the public would start buying as well reducing the burden on taxpayers. Historically this kind of deal has been profitable for governments in the cases that I know of (in banking), while at the same time keeping more jobs and thus reducing economic impact of unemployment.
They don't really need a bailout to stay in business. The grant money for employees is contingent upon them keeping open flight routes that they'd otherwise close. Sec. of Transportation wants low traffic (small) cities to have access to medical supplies and whatnot (at least that's what she says, of course she's pro-business as well).