it will be worth telling the housing / council tax benefit people about it as a 'change of circumstances' rather than assuming that the various bits of the DWP will just tell them - they might, but if there's a gap between the ESA people telling them you've been signed off and you making a new claim based on pension, you may not get backdating for the bit between the two.
if you're getting ESA now, may be worth exploring if your health condition / disability or whatever (i'm not asking for detail) would qualify you for
attendance allowance once you turn pension age.
and if you'll be on a low income (again, i'm not asking for detail) then may be worth looking in to
pension credit (it replaced the old 'supplementary pension' / income support for pensioners) - I don't know quite how this works, especially if you have a partner living with you, but if you're getting HB for your household, then you might qualify.
broadly, i'd say if in doubt, claim.
age concern have more on pensions and benefits for older people.
and you apply via your local transport authority for your
bus pass - assuming you're in england, this entitles you to free off peak bus travel (i.e. not before 0930 or after 2300 on mon - fri, but any time at weekends) anywhere in England (some councils give discretionary extras, like travel before 0930, or on things like metro / tram / underground etc, but usually only for their local residents, e.g. i think only Nottingham/shire residents get travel on the Nottingham trams.) I'm a bit fuzzy on the rules, but think you need to re-apply as a senior even if you have a pass on disability grounds now.
Scotland, wales and NI have similar, again each valid only within that country - think there are some exceptions for journeys across the borders but i'm not sure.
Senior railcard (trains) or coachcard (national express equivalent) are separate things and need to be bought up front then you get a discount.