Not only can you ask her about a threesome while cooking dinner or milling around in the garden, I think you should. Really, you need to talk about it calmly and in a non-sexual format. If you actually can't talk to her about sex in a perfectly mundane setting, don't swing.
As for suggestions of what to say: I found - "So you know that threesome fantasy we've talked about... how would you feel about doing that for real?" - works well.
As for gauging her interest - do not guess! Listen to her words and accept them at face value. If she says no, accept the no. If she hems and haws, give her time to think about it. If she says yes she would be intersted, talk about it more. If you cannot listen to her words and accept them at face value, don't swing.
Honest, open communication is the key to swinging. No guesses, no impressions, no assumptions... just complete, honest and open communcation in a calm, mundane manner.