Hmm this is a tricky one, and I think in speech people probably wouldn't even notice if you used "with". They would certainly know what you mean.
Having said that, to me it doesn't feel quite right. I would only used "well versed in", and use it with more specific questions than "circumstances", which is quite general:
She's well versed in twentieth-century Russian history.
I'm well versed in the tricks pupils play to avoid doing their homework.
but not
*He's well versed in geography.
*We're well versed in going on holiday. (Though you might say "we're well versed in going on holiday to Bhutan", for example, as it references the specific fact of Bhutan being a notoriously difficult place to holiday in.)
Sorry, that was probably a longer answer than you wanted :-S