Agree with much of what 820KDV has said.
A few thoughts (I've worked for local authorities, bus operators and consultancy over the years) -
There is a shortage of people to do this sort of work - I'm aware of a few councils who advertised since BSIP started, but were unable to recruit someone experienced for what's usually been offered as a fixed term contract. Many people who got made redundant after 2010 have got other permanent jobs (either in local authority transport or something else) or have retired. Bus Centre of Excellence has latterly come along and is helping some people in / move upwards in this line of work.
There's no national standard for job titles, or qualifications required - each council will do its own thing, and while there are remnants of a 'national agreement' for pay and conditions, it's not quite as simple as that, and each council will make its own decisions what pay grade each job goes at. Some councils do things like printed / online timetables and produce roadside timetable displays, some leave that to bus operators. Likewise, some councils have a combined unit that does local bus and education transport (and sometimes social services transport as well) - sometimes in separate teams under one manager, sometimes the same staff members doing a mix of these, some councils have them completely separate.
I expect there will be vacancies advertised over the next few months, now BSIP funding for 2025/26 is confirmed, but wouldn't like to say how many will be short term contracts, as there's no certainty about funding from April 2026 on.
820KDV has mentioned proposals for reorganisation of local government - the main idea seems to be abolishing borough / district councils and putting all the functions in to county councils (where there are still two levels of local authority.) Education and public transport are county council function, but there is some speculation that to make this happen, some of the bigger shire counties will be split in two. For example, a few years ago, the existing boroughs / districts in Northamptonshire and the old county council were abolished, and two new 'unitary' councils for two halves of the county were set up. This model may become more common. I've never been through the process, so don't know how far people just transfer to a new authority, or whether everybody has to apply for new jobs with the new councils and some people find there isn't a chair left when the music stops. (Although there may be chairs left vacant if existing staff decide it's time to retire, or they don't want to move work locations.)
Another strand is the idea of more 'combined mayoral authorities' which take on the public transport function (but probably not education transport.) There's (for example) one that covers Cambridgeshire and Peterborough now, there's speculation about one that would cover Bedfordshire, Milton Keynes and maybe Northamptonshire so presumably would take over the public transport function from the existing councils there.
Depending on where you are, whether you're prepared to move, and local circumstances, all this may offer new opportunities, or may make job security a bit doubtful.
And where franchising happens, there's going to need to be more local authority staff to do contract specifications and all the monitoring / contract management.
Another strand to it is getting the hang of local authority job applications - they tend to have a standard application form (almost invariably online now - it's worth preparing answers in something like Word, then copy-paste, rather than just construct it in the online form, partly in case the whole thing crashes, and also so you've got it as a template to recycle) - and rather than just CV and brief covering letter, there's usually a 'person specification' they put out with the job description that lists essential / desirable skills and experiences they want.
Writing a supporting statement (or whatever it's called locally) that addresses each point in this is key to your application, as that's how they score people to decide who to shortlist for interview. Some people fall flat here because they are too brief, or think it's all about the CV / employment history and this is somewhere to write a couple of sentences about your hobbies and so on. Many councils have guidance on this on their recruitment sites, there's one (Greater London Authority)
here. Sometimes there's a word limit, sometimes there isn't. Personally, going in to reasonable detail hasn't done me any harm. And there can be times when experience / skills from outside paid employment can be worth mentioning.
There certainly are people in local authority transport work whose career started as a driver so it's not impossible. Some local authorities can have a culture where they see themselves as 'a cut above' anyone at the operational end of things, some welcome people with real practical experience.
Best of luck.
