This could be an option depending where in Bracknell you are. Not done the first bit of the BVP so someone else may be able to advise better. Normally pick it up around Farnborough.
Pick up Blackwater valley path, California country park ?. Take this all the way to Badshot Lea.
Quick 5 minute road ride, fairly quite, and onto the North Downs, just outside Farnham. Follow it all the way to St Marthas and pick up the Downs link. Or turn off the downs just after you cross the canal at Guildford and ride the road to Bramley to pickup the downs link.
Downs link, pretty boring but as the name implies gets you to the South downs from the North downs and then drop into Brighton.