Here is a route for you to use a a rough guide, I have cycled most of it at different times, and does keep away from busy roads for the most part. There are in places more minor roads which get you to the same place. Distance is about 90 miles depending on which minor roads you choose to uses.
Hope that helps.
Bath to Rode via B3116.
Rode to Frome Via Beckington.
Frome B3092 to Maiden Bradley then Kingston Deveril
Kingston Deverill to Hindon via Monton Deverill.
Hindon B3089 to Wilton.
Wilton to Salisbury.
Salisbury Romsey via Alderbury, West grimstead, West Dean, Lockerley.
Romsey A27 to Eastleigh.
Eastleigh to Portsmouth Via Bishopstoke then B3937/B2177 to Bishops Waltham B2177 Cosham