when I went on vacation with my family close to bovington we went there as well. We were staying in poole and from there the connection to bovington is really good. about 20 min train trip and 10 min on the bus max and you are there. Poole itself is also nice its at the shore and the area is nice. So if you dont wanna go to tankfest for 3 days or something, you can also do a day around poole.
I stayed in London and took the South Western Railway from Waterloo like 9-10 in the morning when I visited like 3 years ago. Trip takes some over 3 hours. Though, it wasn't under tankfest.