I live in Broadmayne only a few miles away from Eweleaze Farm (as the crow flies). We are blessed with miles and miles of bridleways in Dorset so you are spoilt for choice. I would ride an MTB to make the most of trails, some can be very lumpy especially if they are dried out after being used by horse riders. Best to get an OS map out and have a look, but I would suggest …
Go west along the South Dorset Ridgeway to Hardy’s monument, drop down into Abbotsbury and come back along the quiet back lanes and a few BW’s into Weymouth
Go East on the Inland Coastal Path to Lulworth via the top of Ringstead Bay and come back on the the path that runs parallel to and just north of the ICP.
North is Puddletown Forest, but you won’t make the best of that unless you ride with one of the locals, none of it is sign posted and you could spend a couple of days just exploring
Wareham Forest has loads of gravel trails
The Purbecks are brilliant, loads of trails, some big climbs and descents