Doug Paulley, from Wetherby, was denied access to a FirstGroup bus when a woman with a pushchair refused to move.
Senior judges overturned an earlier ruling which said the firm's wheelchair policy was discriminatory and breached the Equality Act.
He has been granted permission to take the case to the Supreme Court because it raises issues of public importance.
Mr Paulley attempted to board a bus operated by FirstGroup Plc which had a sign saying: "Please give up this space if needed for a wheelchair user".
But he was left behind at the stop because the woman with a sleeping baby in a pushchair refused to move when asked by the driver, saying the buggy would not fold.
The appeal judges rejected Mr Paulley's claim of unlawful discrimination.
FirstGroup Plc has a policy of "requesting but not requiring" non-disabled travellers, including those with babies and pushchairs, to vacate the space if it is needed by a wheelchair user.
In 2013 Leeds County Court ruled FirstGroup's policy was unlawful and said disabled users should have priority access to wheelchair spaces.
However, last year the Court of Appeal said the "proper remedy" for wheelchair users to get improvements was to ask Parliament.
Mr Paulley's case is being supported and funded by the Equality and Human Rights Commission (EHRC).
A date has not yet been set for the Supreme Court hearing.
A man has won a legal battle to have his case about wheelchair access on buses heard by the Supreme Court.