Timbrell's Court. A couple of clues here:
23 June 1785: Bath Chronicle and Weekly Gazette
Monday last a youth about twelve years of age, son of John Prichard, in Timbrell's Court, near the Old Bridge, was unfortunately drowned in the Avon, near Dolemead. His body lay in the water more than half an hour, so that all endeavours to restore him were ineffectual. Dr Luzzatto passing by just as the body was taken out, very kindly directed the usual steps taken by the Mumane Society for the recovery of drowned persons. The unhappy parents are real objects of compassion, having at home the child's grandfather lying dead.
2 October 1856: Bath Chronicle and Weekly Gazette
from an item on the Bath City Act Committee
They had carried out improvements in Lyncombe and Widcombe, at a cost of between £2000 and £3000. Several old houses had been purchased, one of them, the "Royal Sailor" Timbrel's Court had been improved – as much as £3000 had been laid out there.
Items reporting on the suicide of Joseph Eyles in 1869 describe him as living "in Timbrell's Court, Claverton Street, Bath" and at "Timbrels Court, Widcombe". The latter article also refers to the Old Bridge.
And here it is on the large scale OS map of 1886 running ~NS and adjoing Claverton Street, with the Avon and Old Bridge just to the north.
https://maps.nls.uk/view/117878223added –zoomed in:
https://maps.nls.uk/view/117878223#zoom=5&lat=5402&lon=14147&layers=BT