Nice to see a new poster, we don't get many these days.
Yes, Higher Bridge Street led to the junction of Halliwell and Blackburn Roads.
I quickly checked on Google Earth and it seems to show Blackburn Road extending further south than the junction and joining Higher Bridge Street a bit lower down - which probably is what it is now - but it certainly wasn't back when I was growing up.
I can confirm my memory to be right by simply Googling the addresses for both the Wryton Stadium and the Globe Inn, which were both on that stretch of the road, and which both are shown to be on Higher Bridge Street.
It's actually difficult to say for certain which ward Higher Bridge Street WAS in at the time, as ward boundaries are reviewed and moved over time, as all wards have to comprise roughly of the same number of electorate - hence the need to change boundaries from time to time, and even sometimes to renamed the wards to something new.
If you want a definitive answer you probably need to contact the councils, Electoral Services Office as to what Ward, Higher Bridge Street fell under in the years you are enquiring about.
I would think it would have been Halliwell, myself, but I don't know for certain.
I don't actually remember Tobutt's on Higher Bridge Street, I always think of it being up near Asda, so I can't help you out on that one, sorry, unless you again ask the council's electoral Services Office.
I've never heard of Arrowsmith Terrace and after a quick Google looking for it, I've probably found your dad's letter to the Bolton News, in relation to the Albert Inn...
MORE confirmation that the picture of the Albert Inn which I published recently was in Poplar Street, School Hill, Bolton, comes from Mr Wilf Bancroft, of Chorley Old Road.
"I lived in Arrowsmith Terrace as a boy, and Mr Joe Griffiths was the landlord of the pub. In the background of the picture, you can see what I think would be Barlow and Jones's Albert Mill, looking up Duke Street," he writes.https://www.theboltonnews.co.uk/news/5890169.albert-inns-landlord-was-joe-griffiths/
For what it is worth I've supped in the Albert many years ago and here is a picture and write up about it, if it is any help to you, as I assume Arrowsmith Terrace must have been reasonably close by?Albert Inn, Derby Street
The Albert Inn on Derby Street, pictured in February 2003. Note the initials SL on the date stone above the date 1884 (see below for explanation). Picture from bolton.org.uk.
The Albert was situated on Derby Street opposite what is now the Lidl supermarket. The building still stands and has been a restaurant since around 2012 but while the date stone on the side of the pub notes that it was built in 1884 it actually dated back to 1852 as a pub. The stone also includes the initials 'SL' – Sarah Leach, the pub's formidable landlady for much of the second half of the 19th century.