D. radiodurans is capable of withstanding an acute dose of 5,000 Gy of ionizing radiation with almost no loss of viability, and an acute dose of 15,000 Gy with 37% viability.
Much better than we can.
In 2003, U.S. scientists demonstrated that D. radiodurans could be used as a means of information storage that might survive a nuclear catastrophe. They translated the song It’s a Small World into a series of DNA segments 150 base pairs long, inserted these into the bacteria, and were able to retrieve them without errors 100 bacterial generations later.
But 300 years? On a lighter note, Asimov’s Silly Asses reminded me of this Fly, You Fools! comic.