Take the No 56 bus to Exeter St Davids Station:
http://www.stagecoach..._56,%2056A,%20379.pdf
Then travel by train to Gatwick, changing at either Reading or Clapham Junction depending upon which service you use.
For example, assuming that you're on the 0935 (weekdays) Flybe arrival, you'll catch the 1038 bus, arriving at Exeter St Davids at 1108. That will get you on the 1139 train to Reading, arriving at 1315. From there, the 1334 departure will get you to Gatwick Airport at 1450.
You could get to East Croydon at about the same time but the journey is a bit more complex. Take the 1139 from Exeter St Davids, through to Paddington (1344). Take the Bakerloo Line 3 stops southbound to Baker Street and then the Jubilee 6 stops south/eastbound to London Bridge. (alternatively travel via Kings Cross, using the Hammersmith & City Line followed by the Northern Line). Then catch the 1442 service, arriving at East Croydon at 1454.
There are trains on a more direct route to East Croydon (simply changing at Clapham Junction) but not around the time which you're likely to be travelling.
http://www.nationalrail.co.uk/
Chris