It is possible, however it would be a long and fairly complicated journey. You would have to get a bus from Manchester to Macclesfield, Macclesfield to Crewe, Crewe to Stoke-On-Trent and finally...
You can get the train. If you are going from Manchester Picadilly, take the train to Stoke-on-Trent, then take a train from there to Uttoxeter. From Uttoxeter you can then get a bus service to Alton...