I haven't seen mentioned here the fact that there are really several kinds of bivies. One is designed as a stand-alone shelter and is waterproof. Those are heavier and are also prone to condensation. It's also pretty hard to get into and out of one while it's pouring rain without letting water inside. These are used mostly by mountaineers.

Another kind of bivy is meant to be used as a supplement under a tarp. It is water-repellent rather than waterproof, having a waterproof underside and a water-repellent but breathable top side.. It helps prevent splash from hard rain or wind-driven rain from wetting you while you're under the tarp, and it usually has a screened opening to keep off the bugs. On clear nights, you can use it without the tarp for a night under the stars, as it should repel the dew. I tried one of these once and found it also prone to internal condensation. Of course, since I'm an active sleeper, turning over frequently, I ended up with the waterproof side on top, which certainly didn't help the condensation issue! I suspect that one of these would be too warm for Iowa summers. You can prevent splash by using a slightly larger tarp and staking it down to the ground in horrible weather.

There are also "bug bivies" or "net tents," which are made of netting, usually with a waterproof floor, again designed to be used under a tarp. (The waterproof floor replaces a ground sheet.) I strongly suspect that this may be what you're looking for. Mountain Laurel Designs and Six Moon Designs are two outfits that make this kind of bug bivy/bug tent, and of course there are others. Or you can get netting and rig up your own.

I originally wanted to use a tarp plus bivy or bug net rather than a tent. However, I did a bunch of research and found that the tarp/lightweight bivy or bug tent combination weighs as much as or more than the lightweight tents described in the responses above. In my case, I had to consider my dog (since deceased), who was perfectly happy to sleep throught the night in a lightweight tent but kept waking up and waking me up (inevitably just after I'd dozed off!) when under a tarp. (He was accustomed to sleeping in a crate.) So for my needs, I stuck with the tent. I have two lightweight tents, one (expensive!) weighing 17 oz. and the other (cheaper) weighing 27 oz., both including stakes and guylines. I should sell one, but I haven't decided which! The weight does not include poles, as Wandering_Daisy pointed out above, and you bikers certainly do not use trekking poles! However, poles for a tarp will probably weight about the same as the poles available for lightweight tents.

Since the weight of lightweight tarp + lightweight bivy, vs. lightweight tent, differs little, it really depends on which style you prefer.
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey