I was in bed. Woke up to a weird gushing feeling that didn't stop when I clenched (as if to hold in wee, at first I thought I was just wetting myself!). I had no signs whatsoever that labour might be able to start before this. Never even felt any BH that I knew of! Had a bloody show and a clear out within about 30-60 minutes after waters went. Mild period cramps (nothing to write home about, but more cramping than I'd felt my whole pregnancy) started within about an hour of waters going. I was in established labour (contractions about 50 seconds long, ever 5 minutes and getting closer together) about 2 hours after waters went. My daughter was born about 11.5 hours after waters. Pretty quick and straightforward, though I was only 37 weeks, so totally unprepared to have a baby yet!
Honestly, don't worry about it making a mess. It's just clear fluid and it has no smell (assuming all is healthy). Mine soaked the sheet and mattress pad a bit, but no big deal. We just chucked it in the wash. If it had gone when I was sitting on the sofa, I could have done the same with the cushion cover. If you aren't sitting or lying down, your clothes will absorb most of it. It really wasn't gross or messy at all. I had a home birth and the midwives forgot to put much of anything under me, so there was a massive blood stain on the carpet and on the bed. Again, even that washed out just fine and you'd never even know it was there. If you're concerned, you can always put a bed mat under your fitted sheet to protect the mattress. By now, our daughter has also vomited and shit on our bed so many times anyway, that a little amniotic fluid is NOT the grossest thing that's ever happened to it!