Simply having more cyclists around has been proven to make your bike trips safer because cars begin to understand how to share the roads and figure out common cyclist behaviour.
We were in the Netherlands a few weeks ago. I didn't take the picture below, but it's a common sight, especially at commuter train stations. You see more bikes parked than cars parked.
Bike paths are EVERYwhere. Literally. A two lane car road will usually also have another two lanes for bike traffic. When you cross the road, you're just as wary of getting hit by a bike as getting hit by a car. Drivers definitely are aware of bikers, and know how to share the road.
So... what are the stats for the Netherlands? How do they compare?
I don't know the stats on accident rates, but I do know (because I've been an advocate for humanistic and not vehicular cycling for more than a decade now) that the modal share of bicycles (i.e., the percentage of folks who use them to commute) in certain cities in the Netherlands, Denmark, and a few other locations is as high as 40%, which is...40x higher than the overall US modal share, and at least 4x higher than that in our largest bike-"friendly" city here (Portland). But cycling isn't much more common there because random people decided to be badasses; it took a lot of top-down policy shifts to make people feel
safe, which led to cyclists everywhere over time. The key word is infrastructure.
There are blogs that go into this extensively, such as copenhagenize.com (from a technical end) and copenhagencyclechic.com (from a people-focused advocacy end). The thing is, though, in pretty much all of these bike-friendly areas, the cyclists don't do absurd things (as a rule) like dress up in lycra, ride at 15 mph, "take the lane", use HID lights, commute 10 miles to work, etc. That's a very American mindset because bicycling here is fundamentally unsafe because the infrastructure is designed to make things as convenient as possible for cars, and by extension, as inconvenient as possible for pedestrian and cycle-based (and public) transportation. Bike-friendly areas are designed the opposite way in mind. Good bike infrastructure isn't top secret technology, but it does require a willingness to implement it. One obvious example of many is the placement of bike lanes to the right of parked cars instead of to the left, which leads to cars naturally protecting bicycles instead of cyclists constantly at risk of being crushed between traffic. There are many other simple implementations common in bike-friendly environments. As a rule, the US is almost completely lacking in all of them (yes, even in Portland).
Any strategy that asks people to share roads with 30 mph+ traffic is going to fail, and will be reflected in the atrociously low cycling population and the absurd gender- and age-bias in the few who do cycle (predominantly male, predominantly under 40). In bike-friendly cities, you see equal numbers of men and women cycling. You see children cycling and the elderly (yes, 70 and 80 year olds can still ride bicycles if they feel safe enough to do so and see others doing so). It's a different world. Telling people to toughen up and brave high speed traffic and engage in several mile commutes is going to keep cycling right where it is in the US--pretty much nowhere. Like every other serious issue facing society, it's not one we're going to solve by individual badassery, which is why the very idea of Mustachianism (save 25x your income and retire at 40!) is always going to fail at the societal level vs larger actions (like pensions, social security, living wages).
I've gone on too long; here are a few pictures from CCC.
Note how wide the bike lane is. Note how it's not part of the street. Note how there's an equivalent lane on the other side of the street. Note how the cyclists aren't dressed like they're Doing Serious Business, but more like...pedestrians, or car drivers. Note how he's on a bike capable of carrying a car seat, or at least two kids not in car seats.
Note the big, bright, blue bike lane. Note how it's separate, yet parallel, from an equivalent crosswalk for pedestrians, underscoring how both are acknowledged parts of the community. Note how the cyclist on the left is female, and wearing high heels (i.e., going to work).
It's not as simple as telling people to just get on their bikes and stop being wusses. Our inability to grasp this here is part of why they also have things like universal healthcare and affordable college educations; they haven't been brainwashed (yet) into thinking societal failures are just failures of the individual.