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This entry is probably not him as the name has no details and there's some people with these abbreviations listed as ratepayers.  Seems unlikely for him to be a householder.
Victorian Directory (Sands) 1925,
W'm J Batemann, 49 Honeysuckle St, Bendigo

However, electoral rolls show:
1930 Electoral Division of Parkes
William Jesse Bateman, Wombin, station hand

This newspaper article has a description of the 'station' from 1901
https://trove.nla.gov.au/newspaper/article/112367740

There are quite a few mentions of Wombin if you search Trove newspaper site, but no mention of 'Bateman', that I could find.

Googlemap shows it as Wombin, Goonumbla NSW 2870 about 40k from Parkes; there's an aerial view but it's not very clear.  Lots of copper/gold mining in that area now, and a solar farm apparently. 

Parkes itself has two main attractions: the Parkes Observatory (The Dish), a world-renowned radio telescope that played a crucial role in the Apollo 11 Moon landings, and the annual Parkes Elvis Festival, a massive celebration of Elvis Presley's birthday, which attracts thousands of fans. Other notable features include the Henry Parkes Centre, which houses the King's Castle Elvis Exhibit and the Parkes Motor Museum, and the region's history of gold discovery.

Judith

Trove has a death notice for her
https://trove.nla.gov.au/newspaper/article/32656947

MUNRO.—On June 3, 1932, at 18 Solomon-street, Cottesloe Beach, Elizabeth, fond sister of Professor James Park, of Dunedin, New Zealand.
Inserted by her devoted niece, L. Gregg.

Cottesloe Beach was the name of a suburb of Perth which is now known as Mosman Park so she didn't die actually at the seaside! 

Googlemap shows a mix of older housing and 'knock-down-rebuilds' in Solomon St, Mosman Park.

Adding:
There's a Funeral notice on the same page on Trove.
MUNRO. — The Friends of the late Mrs. Elizabeth Munro, of Aberdeen, and late of No. 18 Solomon-street, Cottesloe Beach, are respectfully notifled that her remains will be interred in the Presbyterian portion of the Karrakatta Cemetery. The Funeral is appointed to leave her late residence, No. 18 Solomon-street, Cottesloe Beach, THIS (Monday) MORNING, at 11 o'clock, arriving at the Cemetery at 11.25 o'clock.
JOSEPH C. SEMKEN, Funeral Director, Fremantle and Cottesloe. Tels. FM2682 and F1066.

It would seem that she died at home.
Judith

Morling Lodge was an aged care facility with independent living units and a nursing home in Canberra. Now replaced by a newer property.

Judith

Thanks wivenhoe. 
Very annoying that death registration in England doesn't ask for parent names!

Trying to put a few snippets together.

So Sarah MULEEN, who is a witness at the Caroline/Francesco marriage is Caroline's stepsister, previously Sarah Jane BRYANT.
At her marriage to Francesco Yates, Caroline gives her mother's name as Kate McQuinn.
Sarah Jane Bryant, on her own marriage certificate, gives her mother as Kate Maguire.
The marriage of Thomas BRYANT in 1860 is to Celia MAGUIRE and later children to Thomas give the mother's name as Celia.

Just a thought - is it possible that Caroline's mother, shown on the index for Caroline's birth as "Catherine" is the same person as the Celia Maguire that Thomas marries in 1860.  There is no evidence for a marriage between Thomas and Catherine, nor a death for Catherine, Caroline's mother.

However, the newspaper reports found by Sue clearly state that Sarah has a stepsister.

Just a snippet which may be of interest - or not! And no help with Caroline

This birth (from Thomas' second marriage) in 1864 (#A5508), registered Bathurst, for
Sarah A BRYANT, parents Thomas, Celia

This marriage would seem to be the same female: at Waterloo (Sydney), reg 3428/1885
John MULEEN, Sarah Ann BRYANT
The image for this marriage shows Sarah, aged 21, born Bathurst, with parents Thomas Bryant and Kate Maguire, Thomas' occupation is given as 'butcher'.  So it's possible that 'Celia" may have been known as Kate - or possibly, incorrect information given by the bride.