At the risk of upsetting everyone (again) I'm not convinced that accounting measures (such as efficiency measures to improve margins and reducing pension deficits) or the business opportunities available to a PE owner, will solve the fundamental problem of First Bus. Looking at what is reported here (and elsewhere), and not just observation, that seems to me to be trying to do too much with too few resources. The result, unsurprisingly, is that the business is a mess. It didn't happen overnight; and it won't be cured overnight.
As far as First themselves tackling that issue they seem not to recognise it, let alone be willing or able to address it. And as far as anyone else is concerned, I'm far from certain that their best option is to take over a First OpCo with all its issues rather than start from scratch or expand the existing competition. First may well have lots of "interest" (as I would expect) and I would be shocked if they didn't. An "expression of interest" gives you nothing to lose; even the politicians have realised that one, like with their "promises". The hard bit is in turning that into a deal, once they get underneath the surface of the operation and perhaps even actually have to deliver.
As it's the season, maybe it's an analogy that Baron Hardup didn't have too much luck with the cosmetics on the ugly sisters, to attract the Prince Charming. Perhaps First need the Fairy Godmother? And I don't think that's a Council, transport authority; nor Boris or Jeremy (fortunately or unfortunately - depending on your point of view, I suppose).
I'm not sure what is in prospect to make the existing First Bus operation a better business prospect one or even two years (or longer) down the line. I can perhaps think of a few things (or just plain neglect) to make it worse. I think that everyone (at least outside politics) has had their fingers burnt once too often to just blithely assume that anything is solvable, whatever the business theory teaches.