If you walk across the road from the Ramada (A23) towards Horley, turn right & the CAA is about 1.5 miles down the road. There is a pavement down the A23 for 5 mins, when it ends go through the gate & you are on the cycle path (Route 21 I think). Follow the signs to Crawley & you will be there in 15 mins!
I always use the bike on that route but I will be back on Wednesday & I will take the pooch for a walk so I will time the walk for you.
The Ramada will do transport to the airport, you could take that & I guess you could get on the CAA mini-bus from Concorde House (South Terminal) to the CAA.
A local taxi would cost you no more than £5 (01293 430430) but you would have to book them as they are always busy at that time in the morning.