Thermarest neoair lite full size is only 16 oz. As long as you are not camping in very cold weather, this is what I use backpacking.
Pad 16 oz
Tent 20 oz
20F Quilt 20 oz
For a bike, I would need to buy carbon polls for a few oz. But right around 3.5 pounds
I would consider a hammock before lugging a bed. But a hammock does not work so well out West.