Not free, but The Sussex Bus used to operate multiple Tesco bus services between the Burgess Hill superstore and surrounding villages of Ditchling, Keymer and Cuckfield as well as services into Haywards Heath/Lindfield and some villages near there, too.
The Sussex Bus company provides bus services throughout Sussex including Albourne, Brighton, Bolnore, Burgess Hill, Chichester, Crawley, Cuckfield, Ditchling, Eastbourne, Hassocks, Haywards Heath, Heathfield, Henfield, Horsham, Houghton, Hurstpierpoint, Patcham, Plumpton, Pyecombe...
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They would be asking up to £2.70 for an Adult Single in 2015!
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I'd say a fair few consider Compass's Route 100 which, for some bizarre reason, operates between Burgess Hill and Horsham, via Pulborough and Washington (not D.C.) as a shopper service. I often see people waiting at the Tesco Burgess Hill bus stop for it, and getting off of it.
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I keep intending to do the whole journey, but I haven't mustered up the courage for it yet. I do wonder why this route
exists in its current form. The services almost act like trains by displaying "false destinations" to discourage people using it for travel between Burgess Hill and Horsham itself.
Similarly, the 33 service operated by Compass Bus, ex-Sussex Bus,
ex-Countryliner between Hurstpierpoint and Haywards Heath acts as a shopper service to the Haywards Heath Sainsbury's. You could probably argue
the 40/40X were also similar shopper services but for Brighton.
Back in the day, there was also a
922, 923,
924,
925 and
926!