Many thanks for the thoughts.
Self-driving all the way is not an option, nor is parking at a station in this particular case. But then time is not of the essence in this case either. Eventual solution is taxi from Bowerhill to Melksham Station in proper time for 09:55 (even that's a tenner) and then just over 45 minutes to wait at Westbury.
I've not heard of Uber working locally, and as the Southampton arrival has to work for an ongoing connection, wouldn't risk a first time trial on this particular trip.
Taxi all the way quotes are £179 online (ouch). Didn't ask my local contacts on that one; seems that most of the taxi drivers are out until 2 and 3 on Sunday mornings in our area, and it's hard to find anyone after that time but before mid-day - peak rates or "sorry - not available".
Buses to other places. Yes - we have a rather curious doubling up of services past our place on Sundays at present. There's the 271 Devizes to Melksham Town Centre and the 272 Bowerhill via Melksham Town Centre to Bath - both every 2 hours and because the route was recently split between operators, they do connect. So 4 services at our street end between 09:45 and 10:00. As well as the none-connection at Melksham Station, there's the option of doing the Bath dogleg and having 50 minutes there, or going to Devizes, having 50 minutes there and then getting another bus to Swindon. Traveline actually came up with that latter as an option, but 6 minutes from bus to train at Swindon, then 7 minutes to change at Reading, makes me a bit nervous.
The daily National Express service passes at 07:55 ... and they can offer seats to Southampton with a single change and one hour connection at Heathrow. Not mind-glowingly attractive either! None of the stops on the NatEx is near enough to a station to go multi-modal.
Samples from web site exploration follow to complete this case study documentation; no doubt reports of how it went will follow.
OK - so I should not criticise without making constructive suggestions.
a) If the Devizes to Melksham bus ran 8 minutes EARLIER, it could still maintain the onward connection to Bath. The 8 minutes would extend it to Melksham Station, where it could provide connections from Devizes, from the camp ground at Sells Green, from Bowerhill, and from the new East of Melksham development including the Rugby and Football clubs to the 09:55 train. 10 minutes at Melksham Station, and return via the same route to cater for that new incoming traffic, no loss of Bath connectivity.
Idea was put forward as the Sunday element of our
http://mbug.uk Melksham bus proposals, but the (supported) Devizes to Melksham service has been retendered without asking for a price on our option. "Too expensive" I'm told, and "had to get the tender document out" before we could do an iteration to review why it was too expensive. Monday to Saturday proposals remain on the table; that contract process delayed due to staff sickness and I've a serious worry ...
b) If the Traveline offerings came with a fare quotation for through ticketing at a sensible price, and a guarantee to get you there if one of their connections failed (in other words, if it was joined up public transport thinking) it would be seriously attractive!
c) Westbury connections off the TransWilts. This is one that we're watching for 2019. Weymouth DOES work at present on Sundays, but the TransWilts train turns around at Westbury in the platform just vacated by the departing Portsmouth!
