Hi mate.
Stoke station is probably 20 mins walk to Hanley bus station. (despite it being called Stoke on treat, Hanley is actually the city centre. There's bus stops outside the station so just ask at reception at the station for the bus number into Hanley. They will be pretty frequent.
I've just had a look for you and from Hanley bus station the number 18 leaves every 20mins. Get off at Leek bus station. This takes around 45mins by bus.
That's the closest place to Ashbourne. There is a bus service that runs from Macclesfield - Leek - Ashbourne but it's just by Derbyshire council and seems pretty poor. Because of the time you'll be arriving in Stoke, the next bus journey you can get to Ashbourne is ay 7:50pm. That's the number 118 from leek bus station to Ashbourne station.
My best advice if you definitely can't use taxis would be to spend an hour in Hanley and get something to eat to wast a bit of time. Then get the 18 to leek at around 6:30pm, and arrive at leek around 7:15 in time for the 118 bus at 7:50 to Ashbourne.
Otherwise if it was me I'd go straight from Hanley to leek on the 18 and get a taxi from leek to Ashbourne. It's only around 20 min journey and saves waiting for the 7:50pm bus. I could find out a price for you from a friend if you want.
