Maharashtra State Road Transport Corporation (MSRTC) provides 50% concession to all persons with disabilities. Local transport services, in Mumbai this includes BEST, provide 50% concession to students of government-aided schools but not to home-based persons with disabilities. To avail of this concession, one needs an identity card issued by the department of social welfare and/or certificate from school.
One can buy railway ticket from railway ticket counter (not on line) by submitting a photocopy of the certificate. The original certificate needs to be shown while buying the ticket and also while travelling. According to Indian Railways (For details of the railway circular please see http://www.indianrailways.gov.in/railwayboard/uploads/directorate/establishment/ENG-II/pt1_5.pdf):
In suburban trains, separate accommodation for handicapped persons has been earmarked. Two sleeper class berths have been reserved in all non-suburban trains for persons with disabilities travelling on a handicapped concessional ticket. The person accompanying the handicapped person as an escort is also allotted a berth out of this quota. For tickets issued through Computerised Passenger Reservation System, operators have been instructed to allot one lower berth to the handicapped person if possible. The person accompanying the handicapped person as an escort should be allotted middle/upper berths near the handicapped person, subject to availability.