But the services are privately run. You really think the companies would reduce their profit margins to give people cheaper fares? That's not how it works. This is why rural services are disappearing, because there's no money in it for the operating companies. The only way to run public transport fairly is to make it publicly owned, allow the busy routes to subsidise the quiet ones, and take private profit out of the equation altogether.
I'm pretty sure the private operators could make it work better, but the national operators (First, Stagecoach and co) seem to have figured out a way to make a good profit by engaging in brinkmanship with local councils, running down borderline services by dirty tricks like irregular intervals, clumping (two services on very similar routes within a few minutes), splitting (two services on similar routes but different operators and no multi-operator tickets) and cancelling "evening" services to stop workers on 10-6 or 2-10 shifts using them, to the point where they can get council subsidy by threatening to withdraw the service completely.
It seems to take either a smaller operator like Lynx / Coastal Red coming in and shaking things up (discount for using a multi-operator smartcard, services that call at the hospital instead of trying to get people to buy two single-service tickets) or an operator doing a simple regular all-day "clockface" service that calls at the same point every hour, half-hour or quarter-hour (there's one in the west country but I forget its name) to change things. Then the national operator can no longer count on getting the council subsidy contract if it runs a service down - the challenger may get it instead - and so they seem to actually compete... but then that sometimes results in ludicrous "front-running" where the two operators will keep retiming their buses to serve a route a few minutes before the other... yeah, you're probably right, nationalisation, or at least London/Midlands/Yorkshire-style transport executives is needed.
It probably still wouldn't let us take our bikes on buses, though, as
DVSA is the blocker.
(edited to fix typo)
You can get phone apps that show live running data.
Depends on the service. I have found the First X1 Peterborough-Yarmouth live running data has been a work of pure fiction on at least two occasions this year.