Bikes on which you recline rather than sit upright are recumbent. Recumbent means leaning back in a reclining position.
Recumbent starts like recline, which is an easy way to remember it. Your dad's position in his favorite La-Z-Boy reclining chair? Recumbent. Your position when you lay back on lounge chair at the pool? Also recumbent — and in both cases, these are both positions of comfort.