It's said in TGH that Sheriam is the only one who knew that Moiraine sent Min to the WT, but somehow Elaida learned it (probably because Sheriam did give it away, after all). Moiraine's trust is a bit curious, because Sheriam is even mentioned to be a gossip in NS:
"Siuan even suggested bringing Sheriam into their search [for the Dragon Reborn], and talking her out of it required hours. It was not that Moiraine feared Sheriam would expose them to Tamra, but Sheriam had been one of the biggest gossips in the Accepted's quarters. She never told what she promised to keep hidden, yet
she would be unable to resist giving hints of such a juicy secret, hints that she had a secret, as Siuan should have known
very well. Let others know you possessed a secret, and some would work to learn it; that was a fact of nature."

But as you say, probably Moiraine didn't want to believe that her old friend Sheriam would be a BA. Siuan also trusted in one of her best friends Delana. Will be interesting to see how Moiraine might react to those revelations about the BA after her return.

BTW, that Sheriam likes to give hints about her secrets would explain why she told Egwene about the 13+13 trick to turn a channeler.