I know that the season nearly is over but the nearest bluebells to Cheltenham that I know is in Kemerton woods, just off the A46 towards Evesham. Alternatively, there are some very good wetland wildflower meadows nearby, most notably at Coombe Hill nature reserve and Chaceley meadows, nr Corse Lawn which at the moment are full of Ragged Robin.
Check out both the Glos and Worcs Wildlife Trusts for more info.