Ironically these seem to have reached Bordesley from other closed garages Hockley, Lea Hall and Washwood Heath respectively. Route 8a/c had been Birmingham Central, and IIRC only moved to HY because space was needed at BC for routes from Quinton, another garage that closed.
Regarding Quinton, I remember that they took on some routes from Dudley and most from Harts Hill when they closed in 1993. Practically, if I remember right, it was mainly the routes that served Halesowen and Stourbridge, with the remaining routes being revised and transferred to Wolverhampton and West Bromwich.
Although my memory may be patchy as it was so long ago and as I left the West Midlands in 1998, this is my possible recollection of 1993.
Dudley routes:
126 transferred to Wolverhampton
140/241 went to Quinton
120 and 88 went to Hockley (the only ones to do so at the time)
87 went to West Bromwich, also 247/248 for a short while until transferred to Quinton
282/283/285 was revised to run as 226 between Merry Hill Centre and Bilston, interworking with a route revised 138 Merry Hill Centre - Birmingham via Blackheath and Brandhall. Dudley - Sedgley section covered by revised 541. Transferred to Wolverhampton
257 transferred to Wolverhampton
243 transferred to Wolverhampton, interworked with every second journey of the 558. 243 was later withdrawn daytime but was operated by Stephensons of Uttoxeter for a short while
Harts Hill routes:
137 transferred to Quinton
261/264/265 transferred to Wolverhampton
9 transferred to Quinton
291/2/3/4/5/8/9 transferred to Quinton
245/6 transferred to Walsall, then became incorporated with the 311/313
242 Cradley Heath - Kinver transferred to West Bromwich
240 Stourbridge - Cradley Heath transferred to West Bromwich
Just before I left the West Midlands in 1998, Quinton closed with the Brierley Hill, Halesowen, and Stourbridge routes transferring to Pensnett (as WMT's sister company at the time Travel Merry Hill (formerly Merry Hill Buses) had the garage there), and the Birmingham routes going to Birmingham Central. The 21 Birmingham - Bangham Pit via QE Hospital and the 29 Birmingham - Northfield (The Bell) via Harborne and Weoley Castle went to Yardley Wood.
I don't know if anyone in those parts of the West Midlands can fill in some missing blanks or not.