Another good question! I have to say that if you are a start up and unlucky enough to get bad press then I would go to an expert and ask a crisis PR person to manage it for you.
Having said that, if you are in a bind then the best idea would be not to comment to the media at all and to wait for it to die down. The news is on such a high cycle that even something that seems enormous one week is forgotten about the next.
Once the crisis is over, you should try to get as much positive publicity as you can or google will not be your friend. You will need to counteract any bad publicity with some positive articles and mentions.
The best way to handle bad media coverage is to issue a statement that justifies it explains the negative coverage. There are PR consultants that specialise in crisis PR.
Once you have put your statement out there, you can pitch positive story angles about your business or brand.
I specialise in PR for start ups with limited budget. If the start up has even a small amount of potential to receive negative publicity, I would recommend being proactive and getting statements for media ready to go in case the worst happens.
Wishing you all the best!