It would in normal circumstances be daft for a large bus (though I like the Swiss approach to being able to book a group onto public transport of all kinds). But we're in a situation where a big decker has the capacity of what a small community transport minibus has normally, and it is in my eyes the only sensible way to regulate demand, particularly as queueing in and of itself poses a risk.
You could as an alternative price people off, but first come first served via a reservations system is much fairer.
A booking system would kill off public transport stone dead, even the distancing measures that First are introducing will likely put people off over the coming weeks will worsen the problem. Public transport is what is says it is, a transport system for the public, not some niche product that is capable of carrying around fresh air. Stick the government's "buses / trains bad" messaging (I know that's not what they said, but it is how a good many people are reading it) on top of it and I can see the network collapsing when this is all over. I know in my area despite the often horrific congestion, the bus network has been decimated over the last decade with capacity massively reduced. Northern have picked up some of the slack, but the roads prior to the crisis were a nightmare, and post-crisis are likely to be even worse.
In many areas it isn't double deckers running around carrying a handful of people, many services run infrequently using vehicles like Solos. Social distancing and pre-booking one of a couple of seats that would be available will be the end for many local, and essential services, even if used for a short period of time. The harder we make using public transport as a turn-up-and-go service, the more likely it will be to fail completely. Like a lot of so-called solutions in this crisis, the cure seems to be worse than the problem.