Conditions for cycle carriage vary from one train company to another.
Please check with the train operating company concerned.

Dorset is served by two lines operated by South West Trains 023 8021 3600

London to Salisbury and Exeter via Gillingham (Dorset)

London to Brockenhurst (New Forest) and Dorset:  Christchurch, Bournemouth, Poole, Dorchester, Weymouth

Most trains  take  a maximum of 6 bikes (3 + 3 in separate coaches).
There is no charge but a reservation is needed on the Exeter line.

About 40 bus and coach companies in Britain and Ireland carry bicycles on their services, and find that this brings them additional revenue.
Some vehicles can carry more bicycles than certain railway trains!
Unfortunately none of the 40 is in Dorset, the nearest we know of being in
Devon and Wiltshire.

For routes in Devon check with Devon County Council on 01392 383223

Wiltshire Wiggly Bus 01380 860100

For wider information about bikes on buses and coaches, try CTC
or Traveline 0870 608 2608