As with every form of travel, there is a risk of injury when you are riding on a bicycle. In 2013 there were 743 deaths involving bicycles in the United States. That same year there were about 48,000 reported bicycle accidents. Since only a small fraction of bicycle accidents causing injury are ever recorded by the police, the actual number of accidents is certainly much higher.
The fear of getting in an accident deters many people from riding bicycles. That is especially true in areas where there are no dedicated bicycle travel lanes. Fortunately, many new bike trails have been constructed in Las Vegas in recent years. Maps of these bike trails can be downloaded from the internet. See, for example, http://www.rtcsnv.com/cycling/bike-route-trails-map/
Despite the risks of riding on a bicycle, collisions with motor vehicles are relative rare, and most bicycle accidents can be avoided. Simply paying careful attention to traffic and watching for road hazards can greatly reduce the risk of riding. You can also reduce the risk by riding in the daytime, by staying out of areas where there is heavy traffic, and by obeying all traffic laws. Wearing a helmet has been proven to greatly reduce the risk of serious accident while riding a bicycle.