Hey Stottie
It all depends on how much of the Cowal Way you want to walk, and whether you want to visit the Island of Bute and its capital Rothesay. The 35-minute ferry from Wemyss Bay to Rothesay makes perfect sense. Once there, it would be shame to miss out on the palatial gothic fantasy of Mount Stuart (accessible from Rothesay) and the attractions of town itself, from Rothesay Castle to the Victorian plumbing of the Gents Toilet at its pier. Then walk the West Island Way (or take a bus) to Rhubodach in the north: see map on p56 of our guidebook
The Cowal Way. The 5-minute crossing takes you to Colintraive, from where you face about 8 miles to pick up the Cowal Way at Glendaruel, at first using a delightful coastal road but thereafter you take your chance beside the A886 or perhaps take a bus. It looks like the 477 goes from Rothesay to Rhubodach then from Colintraive to Portavadie, if so it's a rare bus route that crosses the water

However, please check this as I'm just looking at the map and guessing!
The alternative is the CalMac ferry from Gourock/Dunoon (the Hunter's Quay ferry is from McInroy's Point, run by Western Ferries and less suited to pedestrians/public transport though I prefer it when carborne). Dunoon has good bus connections with Portavadie (start of the Cowal Way) and other parts of Cowal: check page 15 of our
guidebook and also the
SPT website.
For what it's worth, if it comes down to a choice between visiting Rothesay and Dunoon, two fine Victorian seaside resorts, I'd suggest that Rothesay has more eccentric points of interest and also lets you sample the West Island Way on Bute.