Bivvy sack. If it's in the snow or it's definitely going to rain, a better Gortex type bivvy is the way to go if a tent isn't possible. But if it's just on a contingency, then get a plastic tyvek-type bivvy to save space. My goretex bivvy was costly and it takes up as much space as a light wool sweater. For plastic, I keep a SOL bivvy. It takes up about the same space as a salt shaker, and its cheap. Again, if the plan was to use it a lot, I'd get a Goretex one like my Bibler. I've used it often and only with outstanding results, mostly in the snow. If there is rain, a picnic table can keep you out of the mud. On the other hand, I would never take the Bibler if I planned to avoid bad weather and had a good chance of doing so.
I have hammocks too. They're fun, but can be difficult to set up well. They're better if I have a vehicle I can tie one end to. The biggest drawback is that when camping, I often have several people and keeping the hammocks together is usually not practical without a vehicle. I should also mention that I wouldn't use bivvies for two or more people either because a tent becomes more space efficient. Hammocks promise insulation from the ground provided an underquiilt, but they don't shelter from precipitation without a fly also. I would definitely consider one as an alternative to a bag and inflatable pad in good weather provided I had a chance of finding appropriately-spaced anchors (not at the beach, desert, sagebrush, praries, etc).
I'm living in a mega drought here in the west and can easily plan my trips around the liklihood of any precipitation. I was going to upgrade my pad to an inflatable after my last trip, and I probably still will but even sooner I can take my hammock. For bike touring, I like to keep out of the dirt. It seems like when I go backpacking, everything is more pristine in the far remote back country up high in the mountains. Along the roadways, it's dirtier. So if I take my hammock, I'll still take an SOL bivvy to keep my bag dry in the event of the unexpected, but I wouldn't use it unless I had to. It's smaller and lighter than any tarp or fly.
If you get a hammock, be sure to test out the suspension lines that you'll use. Paracord really stretches and is useless for this. I like the bluewater tubular nylon, but they can be bulky for backpacking or biking (fine for the 4x4). To trim down bulk and still give sufficient length, consider braided synthetic like like dyneema or uhmwpe. Be careful not to cut trees with it -- the tubular nylon is better for that reason. Make a tree-saver with the nylon and add length with dyneema line.
https://www.rei.com/product/610111/b...ubular-webbing
https://www.amazon.com/gp/product/B0...TF8&th=1&psc=1