Thank you SO MUCH for all of your excellent advice!!
Jennifer, thanks for your thought about taking a direct National Express coach for the journey, but I'm concerned about the fact that this service does not run very often. I would hate to spend the first part of our trip waiting around for the next bus.
Phillip, I'm glad to hear that the full fare for the bus/train trip is not terribly expensive. I guess this is a good thing, seeing as there aren't any advance tickets sold (thank you Marco!)
I have done alot of Googling around, and it appears that there is a company, "South West Trains", that might provide a good option. It appears that with "South West Trains" you can take a Rail air link bus to Woking, and then catch a train from Woking to Salisbury.
The WEB site http://www.southwesttrains.co.uk/SWTrains/TravelInformation/Onward+transport+links/Airport+links.htm has information about this.
Have any of you used "South West Trains"?
By the way, we will not be traveling on a Bank Holiday weekend. After reading about this holiday, I scheduled our plans to avoid this very busy sounding event. It rather sounds like the Memorial Day and Labor Day weekends (CRAZY busy, crowded, etc) here in the States.
Thank you again for all of your information!!