It seems there will be some train services on Saturday 13th May.
Looks like first train from Chesterfield at 09.13 to London St Pancras, then take Underground to Paddington.
Several trains per hour to Reading; thence hourly service to Wokingham, which seems to be the nearest you will get by train. (Wokingham is the station before Bracknell). There is a bus - service 4 or X4 by Reading Buses - every 20 minutes from Wokingham to Bracknell. N.B. the 4 & X4 bus start from Reading.