I live in the dutch city of Eindhoven and it's both convenient to have a car and convenient to ride a bicycle. This is possible as long as you invest as much in bicycle infrastructure as you do in car infrastructure.

When a road becomes too wide to cross by bicycle the city here either builds a wide bicycle tunnel or a suspended bicycle roundabout. Those types of infrastructure are expensive, but it's the kind of thing you get if you don't put all of the city's infrastructure budget into one mode of transportation.

What does a suspended bicycle roundabout look like? Have some pictures: https://imgur.com/a/08RJEsk

Here's the location: https://goo.gl/maps/pBTFJGr9sbVHZeDT6

Here's an example of a bicycle tunnel: https://goo.gl/maps/GzAvRCMi1BoxLXgdA

And here it is from the cyclist's perspective: https://goo.gl/maps/mzogX37mqRqrK1JY8

And we also have bicycle roundabouts with tunnels: https://goo.gl/maps/ui28SMbKbXjbvevr5

Did you accidentally cut a freeway through your city? Just build a bicycle bridge over it: https://goo.gl/maps/WqLgJdhsTsr5sufE9

Of course you do need to make sure that there are actually places worthwhile going to within a convenient cycling distance. Which involves building lots of multi-family housing at the edges of downtown. With shops located within those neighborhoods. Rather than huge suburbs with exclusively single-family homes requiring a car to even do grocery shopping.