Depends where in Churchdown
First PLEASE DO NOT EVEN CONSIDER THE A40 Golden Valley!!!!! There are probably more unpleasant and dangerous roads in the UK,but…
Obvious is the old Chelt Road, it isn’t that bad. and there is a bus lane from GCHQ most of the way into the town centre. That is the fast direct route.
Alternative, i know the out not the in, turn off down the Hatherley road, cut through the reddings, the round the back of staverton airport and into churchdown that way.
OR could stretch by aiming for shurdington and coming into chelt on the A46, but it is IMO not as nice a road as the old Gloucester Road.
Likewise you can stretch and head for Combbe hill and come on on the A38/Tewskesbury Road after cut through down hatherley at Bricklehampton Golf Course.
Apparently there is a cycle path somewhere around the airport.
Basically from Cheltenham to Gloucester, there are two sensible direct routes, and you live on one of them.