Competitive swimming ingrained the habit of timing breaths to coincide with certain frequencies of motion. Now I do it for just about everything, swimming, cycling, running, lifting, even snowboarding if it's a particularly challenging run. That said, if you're pedaling at high cadence
"For instance, that always exhale with the same-side down-stroke, and they often breathe in for half a stroke and out for half a stroke."
will very quickly lead to hyperventilation. Normal breathing in a healthy adult at rest is 12-16 breaths per minute, or one every 4-5 seconds. 90 RPM would translate into 90 breaths per minute.