You can take a bus from Twickenham to Sunbury-on-Thames via Feltham Station Victoria Rd in around 35 min.
How to get from Twickenham to Sunbury-on-Thames
From Twickenham train to Feltham Station Victoria Rd then line 235 bus to Sunbury, Croysdale Avenue. 20 min £6. From Twickenham, York Street Twickenham line 490 bus to Feltham Station Victoria Rd then line 235 bus to Sunbury, Three Fishes. 35 min £4. From Twickenham taxi to Sunbury-on-Thames. 11 min £28. From Twickenham drive to Sunbury-on-Thames. 11 min £1.