I also think it depends on the area.
This is it in my area: https://www.swansea.gov.uk/buspasses
Perhaps you can find a similar page for your area?
There's also this, same website, in the FAQs:
Applying because of a disability
For those automatically entitled to a bus pass the applicant must be in receipt of one or more of the following state benefits:
Personal Independence Payment (PIP) with 8 or more points for "Moving Around" or 12 points for "Planning and Following a Journey".
Higher Rate Mobility Component of Disability Living Allowance (DLA) as advised by the Department of Work and Pensions (DWP)
War Pensions Mobility Allowance
An award under Tariffs 1-8 of the War Veterans Compensation Scheme (AFCS)
NHS Registration card or Social Services Registration letter stating the person applying is registered with one or more of the following disabilities:- severely sight impaired, sight impaired, profoundly / severely deaf, without arms or long term loss of use of both arms.
Applicants unable to drive due to their disability must provide a letter from the DVLA stating a licence application has been refused or an existing licence has been revoked for at least 12 months or more.
Based on the above, I'm not eligible for it, in spite of the fact that I have moderate-severe fatigue which can be debilitating + mobility issues and if I walk for more than ~20 minutes a day, I get worse and there's a chance I might not be able to do things normally if I keep it up for too long. And I doubt there's any chance PIP will ever give me points for mobility :/
Asking your local council sounds like the best bet.