Just to the timeline at the link that was posted by diddymiller:
The site of the Bird in the Bush is plot 14 on the tithe map of July 1842:
public house & garden (20 perches)
owner: Earl of Durham
occupier: Joseph Thomas Robinson
Robinson must have recently taken over:
24 April 1841: Newcastle Journal
FOR SALE BY PRIVATE CONTRACT
[a list of lots including a brewery in Newcastle and six pubs including:]
10. All that PUBLIC HOUSE, situated at Penshaw Staith, in the County of Durham, held by Lease for Three Lives under Lord Durham, and known by the sign of The Bird in the Bush now in the occupation of Mr. Geo. Walker.