A rather informal way of saying this, and this has a whiff of slang about it can be:
I bunked with her
Which, to me at least, doesn't suggest sexual contact. In the UK, you might also say:
We kipped in the same bed
Probably owing to the fact that kip, as a noun, means bed, there is no real suggestion of sex here, too.
But generally, I'd simply say what I mean:
We slept in the same bed
We shared the bed, [optional: and slept]
Mind you, if you emphasize "and slept" too much, you may get the odd cynical look from people, generally accompanied with the "ri-ight, you just 'slept'" smirk. Just say you shared the bed in a neutral, factual sort of way, and specify you just slept if you notice people are thinking you didn't get as much sleep as maybe you did :)
Ah well, all in all, the moment you talk about 2 people in the same bed, there's bound to be a couple of people that'll think more of it. A dirty mind is a joy forever, as my parents used to say, and you can't do right by everyone.
If you're worried about people taking it the wrong way, you could just shut them up and turn the "joke" on them. Instead of wrecking my brain trying to find a non-sexual phrase, I'd probably look into phrases concerning jealousy, and what words there are for people who haven't had any in years...