Pensioners are complaining that the Vale of White Horse District Council has refused to copy other authorities in subsidising an extra 30 minutes for the new bus pass scheme.
The new national scheme launched yesterday allows anyone over 60 or who is disabled to travel free on local buses throughout England between 9.30am and 11pm.
Oxford city and South and West Oxfordshire district councils are funding their schemes to start at 9am - but the Vale and Cherwell district councils have refused to follow suit.
Pensioner Ann Marshall, of Meads Close, in Drayton, said: "I question the need for the travel scheme to run until 11pm. Do many senior citizens use this?
"Occasional late evening travel could be met more readily rather than the expectation that senior citizens should finance regular GP and hospital visits in the mornings."
Lewis Beadle, 65, of Steventon Road, Drayton, added: "I am a bit miffed. I think it should be the same - it is advertised as a national bus scheme so it should be the same everywhere."
Peter Pitts, 65, of Adkin Way, Wantage, said the changes would affect anyone wanting morning appointments at Oxford hospitals.
Marcham Parish Council has also written to the Vale councillors to ask for a 9am start.
The Vale's old bus pass scheme allowed free travel from 9am, but council leader Jerry Patterson said the cost had fallen entirely on council tax payers.
He added: "The greater flexibility of the new scheme should more than make up for the loss of half an hour travel time."
A John Radcliffe Hospital spokesman said patients could usually choose appointment times that met their travelling needs.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article