I'm a subscriber to the British Newspapers Archive, and was inspired by this question to do a search for "replacement bus" across the whole of the archive. Already in the first few hits, I've found a couple of things which touch on points made above:
"RAILWAY CLOSED TO PASSENGER TRAFFIC: The Cheshire Lines Railway between Cuddington Junction, on the main Manchester-to-Chester line, and Winsford has been closed to passenger traffic and the train service from Winsford and Whitegate stations will replaced by a bus service connecting with the main line trains. The Cheshire Lines Committee announced a month ago its intention to close the branch on line December 31 [1930], and there has been strong opposition from the Winsford District Council, the Ratepayers' Association and the Co-Operative Society, but all efforts have failed to alter the committee's decision. The Urban District Council, however has not relinquished the fight and is seckmg counsel's opinion on the legal position. The branch line had previously been closed, but in 1890 the Canals and Railways Commission ordered the resumption of passenger traffic." (From the Dundee (!) Evening Telegraph, 1st January 1931)
"A 58 years’ record was broken by yesterday’s temperature in London. Not since 1871 has day temperature of less than 29 degrees [Fahrenheit] been recorded in Loudon the middle ten days of February. One remarkable proof of the strength of the frost occurred on the main Southern Railway line between Broad Clyst and Pinhoe, Devon, where it fractured a rail. Traffic was confined to one track, while the broken rail was replaced." (From the Sheffield Independent, 13th February 1929, backing up the point about alternative routes, wrong-line working etc.)
I'll see what else I can find! (There was also one for our Disputes and Prosecutions board: a 14-year-old boy defrauding a bus company out of two and a half pence by travelling on somebody's season ticket he had found and altering the name, in 1948!)