No, they did not meet in a race before the Preakness.
Barbaro was undefeated. So, if Bernardini had met Barbaro, we would see "Barbaro" in Bernardini's past performances. But Bernardini only lost one of his 3 pre-Preakness races, and that was won by Exclusive Quality.
I have the Preakness PP's on my computer as part of DRF's "Formulator 4" software. I'll see if I can upload a screen save.
--Dunbar
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