I suspect you've left PrintError => 1 in DBI (which is its default value). This means DBI is warning, not dying and the eval block doesn't trap warnings -- they'll go to whatever your $SIG{__WARN__} handler is (which is probably the default and is printing to STDERR.) Set RaiseError => 1, PrintError => 0.

I don't know anything about BioPerl but expect it's also warnings.