Hi .... I was a single mum for a long long time before I became a stepmum, and my ex met someone serious a while before I did again. I admit it felt ... I suppose .... odd to think of my son off out with not only his dad (which wasn't odd) but also another adult whom I'd never met. Thing is though, whilst I had no objection to meeting her per se, say, if we bumped into each other, I wasn't sure it was actually necessary to do so as I didn't imagine, whatever his other faults, that my ex would introduce anyone unsuitable or dangerous to our son because he loved him too and wasn't irresponsible in that way. Consequently, I've only ever spoken to my ex's wife over the years on the phone, in a casual, leaving messages sort of way, where we have both been perfectly polite. If I ever do meer her we shall probably make a lighthearted remark that it's "about time" or something but nothing has ever given me any concern about her.
Realistically, if I had asked to meet her I'm not sure what it would have achieved. She was almost certainly going to be nice - had she agreed - as no-one in that situation would behave like a hideous monster and just suppose if I had taken against her for some reason .... what would I do next ? Demand that my ex dump her because I didn't like her ? .... which would have made future communication with my ex fun I'm sure. By all means, if you close enough to each other that it's likely you may meet casually one day, make polite conversation, offer a cup of tea or whatever, because there's absolutely nothing wrong if all the adults involved with your son can get on amicably but I guess what I'm saying is that it's not actually necessary and neither is it something you can insist upon.
By contrast, my DP's ex demanded to meet me - but only after I'd been called a slag, whore etc, my son had been called a bastard, DP's children had been told ridiculous lies about us both and 101 other sorts of s**t-stirring ...... so funnily enough I declined the invitation as I knew that her motives for meeting me weren't good. I suspect she'd have either had a go at me for some imaginary reasons and/or forever more slagged off aspects of my appearance and so on. Ten years on and we have never met and I have no intention of doing so. Despite all this, DP was repeatedly told that he'd be failing the children if he didn't immediately dump me at the start of our relationship. Ho hum. Conversely, DP's ex has had, errrmmm, several "friends" who he's never met - so complete double standards I'm afraid and an example unfortunately, of a woman thinking she knows best because she's the mother, whereas a father's judgement can't possibly be trusted.