What is the smallest size pot I can use for a Bush Early Girl tomato plant?
Seven gallons, probably. Depends though, how much fruit do you want the plant to produce?
You can also prune it and take that "Bush" out of the name >.
I grew four bush early girls in a 25 gallon container a couple years ago. They grew about four feet tall and produced a huge number of baseball-size tomatoes. At their peak, I estimate that each plant had more than 20 ripe tomatoes on it. Since they are determinate tomatoes, the harvest comes in a rush, but the plants continued producing for at least six weeks.
My guess is that you could grow one plant in a 5-gallon pot and get a decent yield if you feed it very well. Seven gallons would probably increase your yield. By the way, I got a Topsy Turvey upside down planter for Mothers Day that year, so I had to use it. I grew one bush early girl in it, and that one only produced about 8 tomatoes, 3 of which were very small. I think it only held about 3 gallons of soil, and it was very difficult to keep watered. Fortunately, the second year I tried to use it, a squirrel attacked it and I was able to dispose of it without breaking any small hearts.