Nothing as early as you want, here's the pre-war history of the Cotteridge - Northfield route:
20/3/1929: New service
18 Kings Norton (Green) via Pershore Rd South, Watford Rd, Northfield Rd, Bunbury Rd, and Church Rd to Northfield (Bell Inn).
5/2/1930 Service extended from Northfield via Bristol Rd South, Cock Lane, St Helier Rd to Barnsdale Crescent. (Cock Lane is now Frankley Beeches Road)
(30/7/1930 Service extended from Kings Norton (Green) via Redditch Rd to West Heath (Redhill Rd) as service 23.)
1/9/1930 service extended from Barnsdale Crescent via Barnsdale crescent, Basil rd and Trescott rd to Borrowdale Rd.
19/11/1930 Service extended from Borrowdale Rd via Trescott Rd to Fitzroy Rd: and from Kings Norton via Wharf rd, Parsons Hill, Monyhull Hall Rd, Brandwood Rd, Woodthorpe Rd, Taylor Rd and Haunch Lane to Yardley Wood Rd.
27/7/1931 Service diverted from Barnsdale Crescent via Hoggs Lane to Trescott Rd; omitting Basil Rd.
1/4/1932 Service diverted from Trescott Rd via Norrington Rd and Borrowdale Rd to Trescott Rd.
25/4/1932 service diverted from Norrington Rd to Borrowdale Rd. Return via Borrowdale Rd to Trescott Rd.
28/6/1933 Service diverted from Barndale Crescent via Basil Rd to Trescott rd on journeys to Northfield only.
?/?/1942 Service diverted from Bristol Road South via Frankley Beeches Road, Hoggs Lane and Basil Road to Trescott Road. Return from Trescott Road via Hoggs Lane and Frankley Beeches Road to Bristol Road South etc.
Cotteridge and Selly Oak were linked by bus route 10 in 1923 (later became 11, the Outer Circle) otherwise it was tram from Cotteridge to Pebble Mill Rd, then the Tram to Selly Oak (where feeder bus services ran to Northfield, Rednal and Rubery until the tramway was extended to Northfield on 1/10/1923, Longbridge 17/12/1923, Rednal 14/4/1924 and Rubery 8/2/1926).