If you don’t mind the confined space, bivies can certainly work for bikepacking. Enlightened Equipment makes the Recon bivy, pretty highly regarded, and weighs just under 6.5 ounces. Mountain Laurel Designs just came out with a new bivy, the MLD Bug Bivy 2 that has a bit more room than a normal bivy and weighs 7 oz. Borah's bivy is also well thought of. Put any of them under a cuben tarp and you can have a system that weighs less than a pound. I've used bivies with a tarp in spring/fall/winter (I generally don't backpack in summer). They won't increase your warmth very much at all - they're mostly, IMO, for keeping the bugs at bay and keeping rain spray off your quilt/sleeping bag. (If you haven't looking into quilts as well, you might consider one. It's all I use until the temps get below 25 degrees.)

Another way to go, zPacks makes cuben shelters that are spacious and light. And expensive. I own and use a zPacks Duplex as a solo shelter, which is a palace for one person with plenty of room to move around and store your gear in your shelter, and it only weighs 21 oz. including stuff sack and guylines. I’ve used this shelter in the forests of Pennsylvania and the mountains of California, Montana and Idaho. My favorite shelter of all time at the moment.

Cuben is, of course, quite expensive. The base Duplex costs $600. So not for everybody.

Somewhat related, there is a great site for bikepackers if you haven’t heard of it: called Bikepacker :-). You can find it here.