I thought of a new angle on just how badly most modern cities have let people down by not enabling safe biking.
Most cities have at least some bus service, whether as a semi-credible public transit system or as a sop to the poor and elderly. How fast are these buses? Pretty slow. NYC buses rarely break 9 MPH / 14 KPH though they're especially slow. City Observatory has easily-graphable data for multiple US cities, 2000-2013; the mean and median are 13 MPH / 21 KPH, big dense cities I'm familiar with are more like 11 MPH / 18 KPH, and very few cities break 15 MPH / 24 KPH. Absolute peak in the US was Salt Lake, almost hitting 19 MPH / 30 KPH for a few years. Even BRT systems around the world rarely break 30 KPH.
Bike speeds vary a lot, but en masse, one source says Dutch riders average 17 KPH. From my experience, it feels hard to go under 15 KPH and stay upright, even on a thick and heavy bike. [Edit: this says 12.4 KPH for the Dutch, and now that I have a bike I see I overestimated my default speeds. I don't know if either Dutch figure is "speed of motion" or door to door "speed of travel".] So being able to bike is like having personal bus-speed service, without the car necessities of a driver's license, insurance, and thousands of dollars per year spent on a car. (Or social cost of the 40,000 lives a year lost to cars, pollution, noise, etc.) Even if buses go faster than you do on a bike, not having to walk and wait means bikes win up to some distance.
Let's do an extremely bus-friendly case. Bike 15 KPH, bus 30 KPH, average of 10 minutes walk and wait to get on a bus. They cover equal distances at
1) 15*t = 30*(t-1/6), t = 1/3 hour, distance = 5 km
. So for trips under 5 km or 3 miles, biking is faster.
If bus speed is 20 KPH and the time is 15 minutes to get on, we have
2) 15*t = 20*(t-1/4), t = 1 hour, distance = 15 km
.
And this has been assuming that your destination is right at your bus stop; in reality there's potentially more delay there. (Also assuming bike parking right by your destination.)
Note what this means for a city planner wanting to reduce car use. You could invest a lot in public transit, including the high capital costs of metro or the high labor costs of frequent bus service... or you could shape your infrastructure so that lots of people view biking as safe and convenient, providing their own bikes (at a few hundred dollars/year) and labor, with your main job doing sweeping and snow removal.
But of course that low financial cost comes at the high political cost of taking street space away from cars. Easier to drop some buses in and call it a day... easier, but not very effective.
This post owes a lot to this kchoze post, on why buses have low mode share in Japan, and arguing buses have little role in a well-designed city (one with good walkability and metro, not to mention attractive biking.) I'd urge you to read the kchoze as well.