No Usable Routes
People get habituated to automobile routes, and it's easy for them to fall into the belief that there is no other way. Get a map of your city or town and explore the roads on the weekends. If your town is small, you can find a free map at the town hall or court house, usually with the city streets on one side and the county roads on the other. The idea is to find residential streets or lightly trafficked roads which parallel the main drag. Towns and older cities have a regular grid, so if one street creates problems, try the next. Newer cities have mile square blocks of mostly dead-end streets with heavy trafficked arterials between. However, by studying a map, it is often possible to find a fairly short route through.
Many roads with heavy traffic are still quite bikeable because they have good shoulders or wide lanes. In riding on such a road, don't hug the edge of the pavement because you will be less visible to motorized traffic. Pay special attention to vehicles that may turn across your path, as some motorists either ignore or fail to see cyclists. Don't ride on sidewalks, however.
A solution that may work for some people is to arrive at work at a different time than eight o'clock and to start back home at a different time. Roads that are dangerous to travel by bicycle between 7:30 and 8:00 AM and between 5:00 and 5:30 PM are often quite safe half an hour earlier or half an hour later. Arriving early provides a chance to wash up and/or cool off