The free travel rules depend upon which council are you are resident in:

Lincolnshire
When in possession of a Lincolnshire Council issued travel pass, OAPs can travel free, but they must be travelling within, into or out of, the county of Lincolnshire.

North Lincolnshire
When in possession of a North Lincolnshire Council issued travel pass, OAPs will be entitled to free travel anywhere within North Lincolnshire.
On through journeys into other counties the passes will entitle holders to free travel to the North Lincolnshire boundary and then half fare from the boundary to their destination, with the same arrangement working for the return journey.

North East Lincolnshire and South Kesteven
When in possession of a North East Lincolnshire or South Kesteven District Council issued travel pass, OAPs can travel free within their district boundaries. In addition, they will be able to travel into or out of their district boundaries on through journeys with a discounted fare reflecting the free travel entitlement for the part of the journey within the district.

Nottinghamshire
After 9.30am Monday to Friday and all day Saturday and Sunday OAPs will be entitled to free travel within, into or out of, the county of Nottinghamshire, provided they are in possession of a Nottinghamshire Council issued travel pass.
Before 9.30am Monday to Friday, OAPs will be able to make the journeys above but will need to pay half fare.

South Yorkshire
After 9.00am Monday to Friday and all day Saturday and Sunday, when in possession of a South Yorkshire Council issued travel pass, OAPs will be entitled to travel free within, into or out of South Yorkshire
Before 9.00am Monday to Friday, full fares will be charged.

Kingston Upon Hull
When in possession of a Hull City Council issued travel pass, OAPs can travel free anywhere within their district boundary. Passes are valid for free travel on through journeys into and out of East Riding provided that the journey starts or finishes in Hull City. (Cannot be used for journeys which cross the Humber Bridge.)

East Riding
After 9.30am Monday to Friday and all day Saturday and Sunday, when in possession of a Green East Riding Council issued travel pass, OAPs will be entitled to travel free, on journeys wholly within East Riding. On through journeys into, or out of Hull City boundary OAPs will be entitled to a discount from the through fare.
When in possession of a Red East Riding Council issued travel pass, OAPs will be entitled to travel free in East Riding and across the boundary into Kingston Upon Hull. Red passes are also valid for free travel on journeys wholly within Kingston Upon Hull.

If you think you may be entitled to a concessionary bus pass, or if you have any questions about your current concessionary bus pass, please contact your local authority.

Lincolnshire County Council - 01522 552222
Nottinghamshire County Council - 01777 713800 or 01623 476800
North East Lincolnshire Council - 01472 313131
North Lincolnshire Council - 01724 296294
South Kesteven District Council - 01476 406080
West Lindsey District Council - 01427 676676
East Riding Council - 01482 393939
Hull City Council - 01482 300300
South Yorkshire PTE - 01142 767575