London bus route 3 runs down the A3 for all of 300 yards in Kennington.
[The 219 runs along a length of the A219 between South Wimbledon tube and it's terminus in Wimbledon Town Centre.] - hadn't spotted someone already got this one.
Buses Excetera's Surrey route 25 runs along the A25 between Clandon and Gomshall.
Clarifying on an earlier post, Solent Blueline ran an X27 down the A27 between Southampton and Portsmouth at some point in the not too distant past.