Per hour it's about equal and that really makes sense since a fatality probably involves a collision, and collisions are mostly caused by inattentiveness or impairment. And would be dependent on the amount of time exposed.

Per mile traveled, three to ten times as many cycling fatalities per mile as car fatalities per mile, depending on which stats you find.

But, you cut it in half just by not riding the wrong way, not riding at night without lights, not riding on sidewalks and not drinking. I had the data to back that up but not at the moment so take it or leave it, or with a grain of salt as you prefer.

Additionally, in urban areas a third of the fatalities are at or near intersections (in NY, almost 90% were within 25 feet of an intersection, but maybe NY is dense with intersections?) In any event we can zoom in on that 1/3 of fatalities by taking extra care at intersections.

With some other risk-shaving - and you can find data to support it if you really dig - most commuters can cut it statistically to not much more dangerous than driving.