Hi to Gloria, Sue and Karen
Assuming that Eliza really is Eliza Bosworth Hodges then we can find out quite a bit about her. She was registered Sept quarter 1880 Worcester, mother's maiden name Anthony (GRO), and we can find the marriage of William Inkerman Hodges to Eliza Anthony in Worcester in March quarter of the same year, (almost inevitably!) - FreeBMD. In 1881 we find them in Pitmarton Rd Worcester (RG11 2913) with Eliza given her full name and the helpful exact age of 7 months. William, Baker, has been transcribed as Wm J (26) but the original could be either I or J, and Eliza is 22. Parishes born (St Peter, St John) are all actually in Worcester city.
In 1891 William has become a dairyman in Birmingham and is married to a Sophia. His 2nd marriage to Sophia Williams was in Birmingham 1890 but his other children (William) Frederick Rach(a)el and John all have the MMN Anthony. All b Worcester. Eliza is Eliza O but it takes a lot of imagination to read that as a B - enumerator's mistranscription? Her mother is possibly the Eliza Hodges died aged 30 1889 Birmingham.
In 1901 the same family also has an Albert, 9 - he turns out to be Albert Inkermann Hodges MMN Williams. No Eliza but I did find her as a possible servant, 20, in Birmingham. In 1911 Wm has the full William Inkerman Hodges for the first time, still in Brum.
William I was registered 1855 Worcester MMN Morgan, which implies that he was the son of John Hodges and Caroline Morgan though usual caveats apply, and I found them in 1871 in the city, the only oddity that William 16 was a Glover, but I can't find this family in 1861. Eliza Anthony I found as a servant age 12 (!) in 1871 and in 1861 with her parents James and Eliza in Powick, just outside Worcester, though born in the city - but no meaningful registration.
I can't see Worcs parish records on A****y but they may be elsewhere. Maybe someone else can have a go.
Chris