Its simplistic to say that 'mum' should always be used in place of 'bm'.
From a poster who is a stepparents point of view, mum is their own mum or could be any other mum in the family.
So 'DSC's mum' is generally possible, except where the children aren't DSC because there is no marriage or its a new relationship or the poster hasn't even met the children yet or whatever.
(And I have seen plenty of people jumping on posters for even using the term DSC it transpires they aren't married to the dad)
Then we have to resort to 'DP's DC's mum' which is where things start to get ridiculous. We could say 'DP's ex' however, in these situations. Assuming of course they were actually in a relationship at one point and it wasn't an accidental pregnancy or whatever. Or that shouldn't be 'DP's widow' which is another real possibility.
Also what term could we use to to replace all the bracketed words in a phrase like 'stepmothers on MN are too quick to take against (posters who are mothers separated from their DC's father whose children now have a SM) and vice versa' ?