I can go to my local supermarket, Home Depot, drugstore, ice cream stand and never encounter any violence. Travel on the bus however and well, the police reports say it's a different story. With the reality? Not sure but every time of been on public transit, it's a cluster of "crazies" mixed in with the general populace.
What this tells me is the problem is not public transit or urban spaces. We need to build a more humane city like what they have in Scandinavia (high public trust, services to keep you from being desperate, respect for common individual property) and the risk of violence will drop both in city spaces and on public transit.
A quick Google search revealed some data collected by the US government on the topic.
https://www.bts.gov/content/reports-violent-crime-property-c...