In Summer 2017 there were two direct buses to Alton Towers:
X52 M-F only from Nottingham (Broadmarsh) at 0915 and Derby (Railway Station) at 0955, arrived Alton Towers 1055. Return bus at 1730, arriving 1830 / 1910. Operated from 27 March to 1 September 2017 except some Wednesdays when the rides are closed anyway.
X32 M-F from Stoke-on-Trent Railway Station at 0915? and Hanley Bus station at 0930, arrived Alton Towers 1025. Return bus at 1720, arriving 1815 / 1828. Operated from 12 June to 1 September, again did not operate when the rides are closed.
X32 Sat at 0930 Stoke, 0944 Hanley, arr 1039. Return bus at 1720 as per M-F. Operated 27 May to 2 September.
The 32A has gone.
The only local bus service in the area surrounding Alton Towers is a dial-a-ride service, who I understand were quite keen to have the revenue from people visiting Alton Towers (Ashbourne Community Transport).
There are 'always' taxis waiting at Uttoxeter Station happy to empty your wallet. Often fully accessible vehicles so they are plated for more passengers than a standard private hire car.
Finally there is a registered local service, operated by Alton Towers Transport, which although registered and claiming BSOG, is for staff only. And is eye-wateringly expensive.
Details for 2018 are unknown as yet.
You will not get a taxi at Ellastone except one that has driven out from Ashbourne / Uttoxeter and they will charge you for that journey.