There is no set time for achilles recovery. You can accelerate your healing time with good nutrition. Vitamin C and a couple of amino acids (proline is the main one) are essential for collagen repair. High blood sugar levels can also lead to damage of the tendons. Smaller frequent meals will help keep your sugar levels on an even keel. If the injury is very severe, running in the water is still possible, just wear a splint to keep your foot stabilized, avoiding excessive plantar flexion.
If you decide to cross train with cycling, avoid
using toe clips. Cycle with the pedal squarely under your midfoot. I coached a runner who made it back after seven years of achilles trouble. I've also seen athletes cure the problem with a simple shoe change. Excessive pronation and bad heel counters can easily contribute to achilles troubles. Newer therapies for achilles now include eccentric loading. You should be able to find information on these methods fairly easily on the internet. Any other specific questions about all of this, just ask.