Pre-Clackmannanshire Bridge I have no idea but post-bridge route sounds fine, though the Bridge-Dollar main road can be quite busy with cars - you can divert up the cycle route just after the bridge and left takes you to Clackmannan - in Clacks go right at clock, straight on at the crossroads and head for Forestmill, onto main road for approx 1/2 mile then turn left after Loganlea cafe for Aberdona, right for Dollarbeg then left for Dollar - much quieter route. After that Pool/Yetts o' Muckhart then up and over Dunning, there is a lumpier (but quieter) road they use on the Kinross sportive which takes you to Bridge of Earn.
This route will give you an idea of the Clacks to Dollar segment.
Don't forget Cafe De Fleurs in Dollar, great cafe stop - tell them Mark from DCC sent you