It's only every hour instead of every 20 minutes, but the 66 goes directly to downtown Providence via I-95 from the airport and will cut your travel time in half for the first leg of your trip.

As far as safety and reliability, RIPTA is very good for an American transit agency in a city the size of Providence. You might encounter some characters on the bus but there are security cameras on all the buses and the drivers don't tolerate bullshit.