I don't have an exact answer - this paper cites bacteria taken from samples of dust at 41km, for example.
http://www.astrobiology.cf.ac.uk/CurrentScience.pdf#search=%22microorganism%20at%20high%20altitude%22
Biological systems are very sloppy in general. We leave our DNA on things we touch as part of our fingerprint, for example. Bacteria from different species "trade" DNA pieces - why superbugs can pass along their resistance to antibiotics to other species.
Anyway, as a conjecture, if spores of fungi or bacteria could pass through (avoid hotspots) in the Van Allen belt by escaping over one of the Earth's polar regions, it's possible that one of these guys could easily get well away from Earth. Unless they were embedded in something that was totally opaque to UV, they would sooner or later have their DNA destroyed. Probably sooner.