If you can head to Purbeck.
Riding closer to where you’re based don’t bother with the Coast Path. 1) It’s very cheeky, 2) Most of it is unrideable.
Really you need a bit of local knowledge. But you have access to a lot of Bridleways where you are which are in pretty good nick this year.
Looking at the OS lots of options depending on how far you want to go. Get on the Ridgeway and ride the inland coastal path (a bridleway) to Hardye’s Monument. Or ride down the hill to Weymouth, follow the cycle trail to Portland and follow the cheeky footpath all round the island.
Personally I’d say take geared MTB. Then again the road riding ain’t bad either…