Free bus pass

I have broken my arm at the shoulder and dislocated it. I will not be driving for a minimum of three months and probably for more time after that..
My doctor has written a letter to state that I won't be able to drive for three months. I'll probably find out tomorrow as the fracture clinic that I probably won't be able to drive for longer than this time as I have quite a serious fracture.

I have applied for Employment Support Allowance as I was in receipt of it before my injury. It's too expensive for me to go on the bus to the gym, which is where I need to go to keep fit and to rehabilitate my other arm (the reason why I'm on Employment Support Allowance).

The fracture to my right arm (my dominant arm) is completely separate to my Employment Support Allowance claim.

I have informed the DVLA that I cannot drive. I informed them over the phone and they said they didn't want the letter that the doctor had written and that I didn't have to inform them after three months but I could just start driving again.
I asked the DVLA to provide a letter that I could give to the application for a bus pass to tell them that I couldn't drive. However they refuse to do this, telling me that the letter from the doctor should be enough. However upon reading the 'Scotland Wide Free Bus Travel for Disabled People or Those Requiring the Companion and Entitlement' application form it tells me that I need a letter from the DVLA. There is nothing on it about a letter from the doctor.

Has anybody had any experience of acquiring a free bus pass without a long-term disability.