Before the Beeching cuts (https://en.wikipedia.org/wiki/Beeching_cuts) a railway line ran directly from Cheltenham to Stratford upon Avon thus enabling some direct trains from Bristol to the midlands to call at Stratford. However today sadly if you want to travel by train from Bristol you will have to travel by train to Birmingham changing stations Birmingham New Street to Moor Street and then catching anther train to Stratford. Doubling back greatly increasing journey times.
The Bristol Spanish Intercambio group successfully travelled from Bristol to Stratford upon Avon and back in a day. For under £12 per head. Including a stop in Worcester.

By taking advantage of the then group save ticket combined (four for the price of 2) with day returns (day returns are often half the price of normal returns) which can be bought on the day we travelled to Evesham via Worcester. We had time to inspect the river Severn

Upon arriving in Evesham we caught the frequent bus to Stratford. We benefitted from reduced fares due to a temporary closure of a bus stop in Stratford. This enabled

Returning from the home of Bard was a different story…