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Found some data on person trips by transportation mode [1] and person miles by transportation mode [2]. Based on that, about 75% of miles are done with car/truck/suv/van, and 0.2% with bicycles; but trips are more balanced, 80% by car/truck/suv/van and 1% by bike.

So I think the fatality rate per trip is probably about the same for bike vs car/etc; but the rate per mile for bikes is significantly higher. It'd be interesting to look at comparable rates from say the Netherlands or another country where bicycling is better positioned.

[1] https://nhts.ornl.gov/person-trips [2] https://nhts.ornl.gov/person-miles