British military strategist is where the Boney Fuller Twitter user takes his name from. If that's correct, this would suggest that it's bone-ee - a reference to Napoleon Bonaparte.

For all the exciting details: http://en.wikipedia.org/wiki/J._F._C._Fuller

That being said, if my assumption above is wrong, then all bets are off (although by the spelling alone, I would still consider it to be bone-ee).