Well bivvying with a bike is maybe the one thing I do know something about. Last year I cycled from St Petersburg to Lands End and then up to the Orkney Islands and also across South Africa. I probably spent 80-90% of the nights in my bivvy bag.
It worked great for us and bivvys have many advantages. I don't think many people have given them a fair chance and so they're a bit understood.
So first the arguments for, or the defense of the bivvy.
They’re adaptability; you can sleep on it, sleep in it with your head out looking at the sky, shelter in it from a thunderstorm, use half of it while your upper body is in bus shelter, use it as a sleeping bag cover while sleeping in a cave, sit up in it propped up against a hay bale, hide behind a hedge or almost anything else and squeeze in a comfortable place to sleep between trees or in moss or almost anywhere.
The advantage over tents is that that a bivvy doesn't need to be erected or pegged out. You can just roll it up and move on if you need to. You don't need flat soft ground where you can put pegs in or anything to tie of guy ropes to. You don't look like you're setting up shop either so people aren’t so worried about you catching some shut eye in the town green.
Tents in the weight range of good bivvy bags are made of lightweight delicate materials. They're the kind of thing's that I end up trying to avoid using for fear of wearing them out, or carry a groundsheet to to protect it. Or a branch can poke a hole in it. They often are very small and/or are single skin and/or have openings so if you wriggle round in the night you end up getting wet.
A bivvy isn't claustrophobic. It's the opposite, it's just a waterproof, hopefully breathable sleeping bag cover, so the world is your tent. Most of the time you can sleep with your head out looking at the stars. And if it starts raining a rain drop on the face always wakes you up and you pull the hood over your head and go back to sleep. If you roll over the bivvy can roll with you.
Bivvy's come in a wide range of prices. From £5 all the way up to hundreds of pounds. The main differentiator in price is the breathability of the fabric, with the most expensive being made out of Goretex and Event. The very cheapest ones are basically plastic bags which I wouldn't recommend for anything but emergency situations. You'd end up pretty wet after a good nights sleep. However for £10-£15 I got one from Mountain Warehouse which was serviceable.
I have a bivvy which is big enough for me to get changed inside and fit all my gear inside if I want. I'm 6'2" and 105kg.
There a few tricks to bivvy bags which I think people used to tents miss out on. The main being airflow. With a tent people seek sheltered locations. However with a bivvy you want a bit of exposure. The best place is probably on top of a hill. Just the slightest bit of airflow over your bivvy can really help the bag breath and make sure you don't have any condensation.
However maybe 5% of the time the elements conspire against you and you can get a bit of condensation in even the best bag and the outside of you sleeping bag can get a bit damp. It doesn't matter though, you still had a good night sleep. If you're only staying out one or two nights it doesn't matter. Otherwise you can stop to dry out your sleeping bag in the sun or spend the odd night night in a hostel/motel to dry things out. Sleeping bags can definitely get wet in tents too when water drips or you end up sleeping against the fly.
When looking for a bag. There's 2 nice features that I had. Most bivvy's are designed for or copied of those designed for alpine use above the tree line where midges aren't a problem. If you want to use your bag in summer I'd look for one with mosquito netting or you're going to have a bad time. The other thing is mine has a little bit of coat hanger wire in the rim. This is nice if you need the top closed during rain and you like sleeping on your back. You can bend the wire to keep the bag off your face. Though I'm probably a front or side sleeper more often than not, so I'm fine anyway.
Well there. That’s maybe everything of use I know in the world