You should ideally bring your own MTB in good working order. Or you can hire one locally and arrange for it to be delivered to Nant BH in time for the start of your course.
You'll also need;
Cycle helmet and gloves (full and fingerless)
Warm outdoor cycling specific clothing such as padded shorts and leggings
Backpack (plus liners - 3-4 small bin bags is fine)
Drinks bottle - 1 litre (or hydration system)
Tool kit, including pump and inner tubes
Waterproof jacket and trousers
Tracksuit or walking trousers (not jeans or heavy cotton)
Tops - long and short-sleeved (ideally not cotton, poor insulation properties, thermal tops are ideal)
Fleeces/warm tops (not cotton)
Footwear to bike in (ones you don't mind getting muddy/wet)
Warm hat, gloves, sun hat/cap
Trainers and a set of clothes for evening activities that can get wet
High factor sun cream (min factor 30)
Sandals/flip flops or spare shoes for wearing around centre
Suggested Additional Items:
Flask Torch (head torch is best, don't forget the batteries!)
Small amount of cash
Notebook and pen
Book, games etc. for the evenings when you're not on activities
Nant BH has an excellent drying room, where clothes should dry overnight if wrung out and hung carefully, but do bring a few changes.
If you are using this course for your Gold Residential for the Duke of Edinburgh's award, don't forget to bring your e-dofe number with you.