Basically, Bostrom postulates that it would be bad news if we were to find signs of life on Mars (or anywhere in our galaxy for that matter). But not because he wouldn't like to see it - in fact I think many people, and certainly most scientists, would welcome such a finding. Rather, he says that
finding signs of life could instead be a very bad sign for our future outlook. Why is this?
Given the vastness of the universe, and the length of time available for other civilizations to develop, one would assume that there is expansive life out there. However we have seen no evidence of it (see: Fermi Paradox). So either something fishy is going on (e.g., we cannot detect alien life) or there simply isn't that much life out there. The latter is much more likely. Bostrom then talks about "great filters" - evolutionary transitions that occur with very low probability. Most life forms die off when they encounter a great filter.
That leaves us with two possibilities:
1) We (humans) have already gone through a great filter, likely one at a very early stage (well before we were humans), and survived. It follows that there will be very few signs of life to encounter since most will have not survived the filter.
2) We have not yet encountered a great filter, but will relatively soon. When we encounter that filter we will likely die off. In this scenario it follows that getting to our current stage is relatively easy (since we haven't passed a filter) and life similar to us should be common.
Therefore, if we were to find signs of life on Mars (or somewhere else nearby), it could be an indicator that we are in scenario 2). After all, having life evolve on 2 planets on the same solar system would indicate that it is something pretty common. And the more developed these life forms are/were, the more likely that we have not yet passed any sort of great filter. That is why the longer it takes us to encounter alien life, the better a chance we have at being in scenario 1). We would be (mostly) alone, but with a (hopefully) bright future in front of us.
Unless there are multiple Great Filters....
Anyway - its a great article and I've probably done a terrible job of explaining it. Just read it.