In our experience bus replacement means no travel. Bus drivers don't like to leave their comfortable seat to open doors for suitcases and stuff.
If you have a prebooked seat from a minline station you may get a taxi replacement, if you are lucky.
If you have time, take an extra day and cycle down. The least steep is south over the hill to Bridge of Earn, then via the main road (A912) to Glen Farg up the B996 (really a continuation of the A912 - as you have to leave the road to continue on the A912). This is a quietish road as most traffic take the M90. It comes out at the A91. From there head into Milnthort, and south into Kinross. Kinross is nice enough with cafes for lunch.
Then follow the road into Cowdenbeath. Heading through Kelty leads to a steep long hill up Hill of Beath. Instead go through Cowdenbeath, and out to Crossgates and south to Inverkeithing. From there go through the town, and head to the bridge on the east side. I'm sure you know the rest. 60km.
As an pleasant alternative, head to Bridge of Earn, (don't be tempted to head direct via Aberdalgie to Dunning - this way lies a very steep climb out of Perth!) then out to Dunning (shop & pubs) and then onto Auchterarder, and out through Glen Eagles to Braco. In Braco head left as you arrive (shop here too) and out to Dunblane through Kinbuck. From Dunblane take the dual carrageway to the M9 roundabout but stay off the M9 and head into Bridge of Allan. Head north of the river to Alloa and Clackmannan and then cross the new Kincardine bridge via the cycle path (marked) and out to Grangemouth and Bo'ness. Finally head into South Queensferry and in on the Route 1. This is a longer route than direct south, but flat and has little traffic to Bridge of Allan. 100km
Dave C