Do not miss that flight. If you have the money get a reliable taxi and head from where you are straight to the airport. You do not want to be late, you do not want to be on a bus full of potentially sick people and you probably should try to avoid contact with as many people as possible along the way.
If you have to take the bus. Give yourself lots of time. Video of traffic in Santo Domingo looks pretty good, in fact I can see concrete streets where normally there is just endless numbers of vehicles. Enhanced procedures at the airport may take longer than usual even with fewer people there to get on a flight.
Depending on the departure time, you might consider traveling to PUJ the day before just to be sure. You definitely do not want to be on a guagua.
The buses are running. Bus schedules are supposed to be unaffected at the moment, but you need to confirm that for yourself as it is not uncommon for buses to be cancelled when there is not enough people to fill one or other circumstances arise.
Good luck.