Who's going to give them a loan? How will they pay it back. How will these new companies pay for new stock while paying off the loan?
This is all standard investment stuff though, surely?
It's a bit like asking who is going to give someone a mortgage to buy a house, how they expect to pay that money pack and how they'll afford anything else in the meantime whilst paying off that mortgage.
If you buy a bus company with (say) ten million quid of annual revenue for (say) ten million pounds (AIUI the old "finger in the air" approach was a relationship between the value of the bus company and the annual revenue, so I'll use it here to keep things simple) then banks will look at the viability of that, decide whether they think you are safe enough to loan money to (and at what rate, depending on their assessment of the risks you are taking)... and you pay those costs whilst paying for various other things (staff wages, fuel, replacement vehicles etc).
Just in the same way that First have borrowed money in the past, First have leased vehicles, it's the way that most businesses operate.
(that's not to say that a management buyout will be better/worse for average passengers than the status quo, I make no judgement here, but it looks to me like a fairly standard buyout is being proposed)