There are several sources of information that indicate that cycling is safer than traveling by motor vehicle. See the table below, and a more detailed explanation on Ken Kifer's How Dangerous is Cycling page. The table shows the risk per hour of exposure to various activities. Note that Bicycling has about half the risk per hour of exposure that passenger cars impose. These figures are for all cyclists.
Experienced cyclists have a far lower fatality rate that pictured here.
Yes, bikes are slower, and therefore you are exposed to the risk for a longer period. Some more, but many more spend far less time in daily transit. The same is true of cyclists. Once the trip starts taking more than half an hour each way, the number of participants falls off dramatically. Therefore, although you may go faster and farther in a car, you will spend about the same amount of time doing it.