Would number 43 be a flat through door number 42?
Extremely unlikely. It is customary for streets to be numbered with even numbers on one side and odd numbers on the other.
Having looked at several maps, I see that Budhill Avenue wasn't on the second edition of the 25-inch-to-the-mile Ordnance Survey maps, surveyed in 1897, so it must post-date that.
Budhill Avenue first appears in the Valuation Rolls in 1905, when there were eleven houses, three works and an office at No 43. See screenshot.
Looking at a more recent map, the odd numbers in Budhall Avenue are on the south side of the street, and Nos 11 to 51 appear to be missing. This is corroborated by the Post Code Directory, which lists odd numbers 1 to 9, 53 to 93h, and 101a to 229.
So I think that 43 Budhill Avenue must have been on the south side of Budhill Avenue, where there is a park shown on the current maps. On the 1897 map, all of the area north of the railway and south of where Budhill Avenue now runs is shown as the Acme Machine Works. See
https://maps.nls.uk/geo/explore/side-by-side/#zoom=18.2&lat=55.85422&lon=-4.16020&layers=168&right=ESRIWorld and
https://www.railscot.co.uk/locations/A/Acme_Tube_Works/Budhill Street is south of the railway line and not connected directly to Budhill Avenue. I don't think it exists any longer. It is listed in the 1905 Valuation Roll but not in 1915, so its name may have been changed.
I have yet to find Budhill Road. No such street is listed in the Valuation Rolls available online, or in the Post Code Directory.