As for additional insurance, that's really between the driver and their insurance company, and the passenger and the driver. If a mandate is needed, per Google looks like some insurance companies offer ride-share for about $150-$200 per year on top of regular car insurance costs.

The State can easily check for these documents every year by requiring an existing $50 business license. 

$50 business license, $150 ride-share insurance, $200 inspection, $35 background check, $175 DOT. 

So, for  about $600/yr we can have sufficiently equivalent "safety" with no additional barriers to entry and much more freedom for individual riders and drivers.