Haywards Heath is on the main Brighton line, with frequent Thameslink services from St Pancras, Blackfriars and London Bridge, plus Southern trains from Victoria. The journey time from London Bridge or Victoria is around 40-45 minutes. On the Thameslink route you can get cheap Super Off-Peak tickets from central and north London (Sat, Sun & BH), but these are not valid on Southern services. Buy a return to Haywards Heath for the walks starting there.
Balcombe is the stop before Haywards Heath, with a half-hourly Thameslink service (hourly on Sundays). Buy a return to Balcombe for the Circular Walk.
At the end of the Alternative Walks Horsted Keynes is served by Metrobus 270, which runs hourly (two-hourly Sun & BH) between Brighton, Haywards Heath and East Grinstead. The bus stops at the western end of the village green, and also at the Bluebell Railway station on weekends. It is quicker to travel back via Haywards Heath but it is useful to be able to return in either direction; the last service to Haywards Heath is at around 6pm (5pm Sun & BH), but there are one or two later services to East Grinstead (2020).
A “Thameslink only” return ticket to Haywards Heath would not be accepted at East Grinstead and you would have to buy an extra single to East Croydon, where the two lines merge.
If you want to abandon the walk after lunch in Ardingly or Little London, Metrobus 272 runs every two hours (Mon–Sat) to Haywards Heath in one direction and Three Bridges in the other.
If driving, Haywards Heath station car park costs £9.20 Mon–Fri, £5.30 Sat, £2.25 Sun & BH (2020). Balcombe station car park used to be free but now costs £2.70 Mon–Fri; roadside parking is available in the village. For the Alternative Walks you could park in Horsted Keynes (there are free car parks in the village and at the Bluebell Railway station) and take the 270 bus to Haywards Heath to start the walk.