You can take a train from Exeter to Swanage via Salisbury, Southampton Central, and Bournemouth in around 4 h 18 min. Alternatively, National Express operates a bus from Exeter to Swanage once daily. Tickets cost $10 - $15 and the journey takes 3 h.
How to get from Exeter to Swanage
From Exeter Central train to Salisbury, train to Southampton Central, train to Bournemouth, then taxi to Swanage. 4 h 18 min £175. From Exeter bus to Wareham, Post Office then bus to Swanage, Police Station. 4 h 2 min £14. From Exeter drive to Swanage. 1 h 44 min £16.