One thing to keep in mind, under the Code once you file BK and have debts discharged you are prohibited from filing BK again (assuming it was a Ch 7) for 8 years. This is why credit card companies are so willing to lend to a discharged debtor. Your bet is safer because the threat of a discharge is gone.
If you have someone who recently filed a BK and have the income to support the rent then I would think they would be a good tenant. I would not let the BK aspect influence me (assuming everything else checks out). A decent place to live with a fair rental value is very valuable to them because they wont be getting a mortgage anytime soon given the BK filing.
While I agree with some of the posts above, BK filers, especially serial BK filers, definitely know the system. I would check PACER to see their BK filing history as part of your regular credit check.