I've tried bivvy bags on a couple of occasions but haven't had much luck with them. My first one I used to carry along with the tent as an emergency back up more than anything. Carried it on several trips and never used it (it was pretty light and packed down small, so it wasn't a problem as an added piece of kit).
So then on a walk of the South West Coast Path, I met a guy who had one, and a little tarp set-up, and just got curious about it. So one evening, (a lovely summer one) I decided to use the bivvy bag. Got settled in ok, enjoyed watching bats on the hunt, zipping by just inches from me, and got to sleep ok. But I was woken in the early hours to pissing rain and a howling gale to find, oh dear, this bag isn't very waterproof! In fact, it wasn't at all waterproof, so there I was, in the pitch black, rain hammering down, pitching my tent outer as the wind tried to snatch it from me - luckily, I was very familiar with the tent and was able to get it set up and dive in for a quick cuppa before settling down again. My other kit was fortunately all also wrapped in waterproof bags, so wasn't a complete disaster.
My second try was with the Rab bag mentioned above. In the Lake District, up by Sprinkling Tarn, near Scafell. Again, it was a glorious summer evening. Didn't rain this time but I found the bag very clammy and restrictive - it wasn't as roomy as the last one. As it turned out, I could've just slept in the sleeping bag without a bivvy bag as it stayed dry and mild all night anyway.
I'm still curious about using various combinations of bags and bashas, tarps or whatever, but don't know if I'll get much opportunity now. For a biking tour I'd rather have a tent though, for that bit of extra privacy whilst on commercial campsites, and as a place to protect all the gear at night. Bivvy bags combined with tarps can start getting up to the weight and bulk of a modern lightweight tent anyway - apart from sleeping under the stars, I don't really see much advantage to them. My tent goes up in a couple of minutes, and is equally easy to take down and pack again.
Stevie, you should have joined the Air Force; when we deployed to the field, we slept in nice, warm, dry German barns - any fool can be uncomfortable!