When we talk about about improved athletic performance, there is a single word which should always lead the conversation: specificity.
The answer is in fact very simple: if you are training for a running event, running should be your primary mode of activity. If training to participate in a bike race, then the bike should be your primary mode of training.
The reason for this is there is little to no transfer of conditioning between different modalities of exercise. This means that riding a bike will never replace running training.
This is unfortunate because it would make our life much simpler if we could ride a bike and, as a result, be sufficiently conditioned to run a half marathon.
The truth is, to run this half marathon, we need to spend a number of weeks conditioning various anatomical structures and physiological systems utilized during running. These same systems are affected in a different way during cycling training, hence, little or no transfer.
Specificity - an extremely simple concept, but an extremely important one.