The amount of rest needed varies greatly by individuals so don't compare yourself to anyone else as an individual. Next, you improve by alternating hard days with easy ones - tear muscle fiber down and then allow for recovery and repair to become stronger. If you don't allow for rest, you prolong getter stronger. Finally if you don't allow for rest/recovery you subject yourself to injury and mental staleness including potentially a form of depression.

If you want to exercise and just did a hard day on the bike or just don't feel like riding, do something else. It's getting warmer and pools will be open. Try swimming as an alternative, or walking, running, lifting weights, etc.