Fares in Bristol and the West of England are easy to find from First's website. I use the mTickets app whenever I travel by bus, as it's cheaper and I like to keep the purse-strings tight, but it took a long time before it moved from weekly tickets to being generally useful.
I have the more bus app installed on my phone for when I'm in the Bournemouth area. They do 1 day m-tickets which are cheaper than paying the driver. I guess for First the ticket availability varies by area. I re-checked the First website for Dorset and still can't find stop to stop fares although a google search found a news story from earlier this year about the fare going up to £5.50.
Maybe next time you go walkabout, it will be available for your trip.
No plans to go back to West Dorset this year or next. My next trip will possibly be to Beaulieu and Bucklers Hard. Seems to be a seasonal route. I'll need to research bus prices from Southampton and how to pay before I get there.